Publications
2023

(2023) The journal of high energy physics. 2023, 3, 16. Abstract
In previous work we constructed an explicit mapping between large N vector models (free or critical) in d dimensions and a nonlocal highspin gravity theory on AdSd+1, such that the gravitational theory reproduces the field theory correlation functions order by order in 1/N. In this paper we discuss three aspects of this mapping. First, our original mapping was not valid nonperturbatively in 1/N, since it did not include non local correlations between the gravity fields which appear at finite N. We show that by using a bilocal G − Σ type formalism similar to the one used in the SYK model, we can construct an exact mapping to the bulk that is valid also at finite N. The theory in the bulk contains additional auxiliary fields which implement the finite N constraints. Second, we discuss the generalization of our mapping to the field theory on Sd, and in particular how the sphere free energy matches exactly between the two sides, and how the mapping can be consistently regularized. Finally, we discuss the field theory at finite temperature, and show that the lowtemperature phase of the vector models can be mapped to a highspin gravity theory on thermal AdS space.
2022

Phases of Wilson Lines in Conformal Field Theories(2022) arxiv.org. Abstract
We study the lowenergy limit of Wilson lines (charged impurities) in conformal gauge theories in 2+1 and 3+1 dimensions. As a function of the representation of the Wilson line, certain defect operators can become marginal, leading to interesting renormalization group flows and for sufficiently large representations to complete or partial screening by charged fields. In some cases, the screening of the Wilson lines takes place by dimensional transmutation and the generation of an exponentially large scale. We identify the space of infrared conformal Wilson lines in weakly coupled gauge theories in 3+1 dimensions and determine the screening cloud due to bosons or fermions. We also study QED in 2+1 dimensions in the large Nf limit and identify the nontrivial conformal Wilson lines. We briefly discuss 't Hooft lines in 3+1dimensional gauge theories and find that they are screened in weakly coupled gauge theories with simply connected gauge groups. In nonAbelian gauge theories with Sduality, this together with our analysis of the Wilson lines gives a compelling picture for the screening of the line operators as a function of the coupling.
2021

(2021) Physical review. D.. 104, 12, 126011. Abstract
We construct an explicit bulk dual in antide Sitter space, with couplings of order 1/N, for the SU(N)singlet sector of QED in d spacetime dimensions (2

(2021) Physical review. D. 104, 12, 126005(14). Abstract
The weak gravity conjecture is typically stated as a bound on the masstocharge ratio of a particle in the theory. Alternatively, it has been proposed that its natural formulation is in terms of the existence of a particle which is selfrepulsive under all longrange forces. We propose a closely related, but distinct, formulation, which is that it should correspond to a particle with nonnegative selfbinding energy. This formulation is particularly interesting in anti–de Sitter space, because it has a simple conformal field theory (CFT) dual formulation: let Δ(q) be the dimension of the lowestdimension operator with charge q under some global U(1) symmetry, then Δ(q) must be a convex function of q. This formulation avoids any reference to holographic dual forces or even to locality in spacetime, and so we make a wild leap, and conjecture that such convexity of the spectrum of charges holds for any (unitary) conformal field theory, not just those that have weakly coupled and weakly curved duals. This charge convexity conjecture, and its natural generalization to larger global symmetry groups, can be tested in various examples where anomalous dimensions can be computed, by perturbation theory, 1/N expansions and semiclassical methods. In all examples that we tested we find that the conjecture holds. We do not yet understand from the CFT point of view why this is true.

(2021) Physical review. D. 104, 8, 086026. Abstract
The superconformal index of the N=4 SU(N) supersymmetric YangMills theory counts the 1/16BPS states in this theory, and has been used via the AdS/CFT correspondence to count black hole microstates of 1/16BPS black holes. On one hand, this index may be related to the Euclidean partition function of the theory on S3×S1 with complex chemical potentials, which maps by the AdS/CFT correspondence to a sum over Euclidean gravity solutions. On the other hand, the index may be expressed as a sum over solutions to Bethe Ansatz Equations (BAEs). We show that the known solutions to the BAEs that have a good large N limit, for the case of equal chemical potentials for the two angular momenta, have a onetoone mapping to (complex) Euclidean black hole solutions on the gravity side. This mapping captures both the leading contribution from the classical gravity action (of order N2), as well as nonperturbative corrections in 1/N, which on the gravity side are related to wrapped D3branes. Some of the BA solutions map to orbifolds of the standard Euclidean black hole solutions (that obey exactly the same boundary conditions as the other solutions). A priori there are many more gravitational solutions than Bethe Ansatz solutions, but we show that by considering the nonperturbative effects, the extra solutions are ruled out, leading to a precise match between the solutions on both sides.
The superconformal index of the N=4 SU(N) supersymmetric YangMills theory counts the 1/16BPS states in this theory, and has been used via the AdS/CFT correspondence to count black hole microstates of 1/16BPS black holes. On one hand, this index may be related to the Euclidean partition function of the theory on S3×S1 with complex chemical potentials, which maps by the AdS/CFT correspondence to a sum over Euclidean gravity solutions. On the other hand, the index may be expressed as a sum over solutions to Bethe Ansatz Equations (BAEs). We show that the known solutions to the BAEs that have a good large N limit, for the case of equal chemical potentials for the two angular momenta, have a onetoone mapping to (complex) Euclidean black hole solutions on the gravity side. This mapping captures both the leading contribution from the classical gravity action (of order N2), as well as nonperturbative corrections in 1/N, which on the gravity side are related to wrapped D3branes. Some of the BA solutions map to orbifolds of the standard Euclidean black hole solutions (that obey exactly the same boundary conditions as the other solutions). A priori there are many more gravitational solutions than Bethe Ansatz solutions, but we show that by considering the nonperturbative effects, the extra solutions are ruled out, leading to a precise match between the solutions on both sides. 
(2021) The journal of high energy physics. 2021, 3, 208. Abstract
We explicitly rewrite the path integral for the free or critical O(N) (or U(N)) bosonic vector models in d spacetime dimensions as a path integral over fields (including massless highspin fields) living on (d + 1)dimensional antide Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bilocal fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on antide Sitter space. Our results provide an explicit (nonlocal) action for a highspin theory on antide Sitter space, which is presumably equivalent in the large N limit to Vasiliev’s classical highspin gravity theory (with some specific gaugefixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1/N expansion, but in principle can be extended also to finite N theories, where extra constraints on products of bulk fields need to be taken into account.
2019

(2019) Journal of High Energy Physics. 2019, 10, 180. Abstract
In this paper, we study the 6d Little String Theory (LST) (the decoupled theory on the worldvolume of N NS5branes) on curved manifolds, by using its holographic duality to Type II string theory in asymptotically linear dilaton backgrounds. We focus on backgrounds with a large number of Killing vectors (namely, products of maximally symmetric spaces), without requiring supersymmetry (we do not turn on any background fields except the metric). LST is nonlocal so it is not obvious which spaces it can be defined on; we show that holography implies that the theory cannot be put on negatively curved spaces, but only on spaces with zero or positive curvature. For example, one cannot put LST on a product of an antide Sitter space times another space, without turning on extra background fields. On spaces with positive curvature, such as S6, R2 x S4, S3 x S3, etc., we typically find (for large N) dual holographic backgrounds which are weakly coupled and weakly curved everywhere, so that they can be welldescribed by Type II supergravity. In some cases more than one smooth solution exists for LST on the same space, and they all contribute to the partition function. We also study the thermodynamical properties of LST compactified on spheres, finding the leading correction to the Hagedorn behavior of the spectrum, which is different on curved space than on flat space. We discuss the holographic renormalization procedure, which must be implemented in order to get a finite free energy for the LST; we do not know how to implement it for general spaces, but we can (and we do) implement it for the theory compactified on S4.

(2019) Journal of High Energy Physics. 2019, 8, 18. Abstract
We construct holographic backgrounds that are dual by the AdS/CFT correspondence to Euclidean conformal field theories on products of spheres Sd1xSd2, for conformal field theories whose dual may be approximated by classical Einstein gravity (typically these are large N strongly coupled theories). For d(2) = 1 these backgrounds correspond to thermal field theories on Sd1, and Hawking and Page found that there are several possible bulk solutions, with two different topologies, that compete with each other, leading to a phase transition as the relative size of the spheres is modified. By numerically solving the Einstein equations we find similar results also for d(2)> 1, with bulk solutions in which either one or the other sphere shrinks to zero smoothly at a minimal value of the radial coordinate, and with a first order phase transition (for d(1) + d(2)

(2019) Journal of High Energy Physics. 2019, 7, 160. Abstract
We discuss 3dN = 1 supersymmetric SU(N) and U(N) ChernSimonsmatter theories, with Nf matter superfields in the fundamental representation of SU(N) or U(N). In the large N 't Hooft limit with fixed 't Hooft coupling lambda these theories have one (for Nf = 1) or two (for Nf> 1) exactly marginal deformations in the superpotential. At finite N these couplings acquire a beta function. We compute the beta function exactly for lambda = 0, at leading order in 1/N. For Nf = 1 we find four fixed points, one of which is triplydegenerate. We show that at large N there are at most six fixed points for any lambda, and conjecture that there are exactly six, with three of them stable (including a point with enhanced N = 2 supersymmetry). The strongweak coupling dualities of N = 1 ChernSimonsmatter theories map each of these fixed points to a dual one. We show that at large N the phase structure near each of the three stable fixed points is different. For Nf> 1 we analyze the fixed points at weak coupling, and we work out the action of the strongweak coupling duality on the marginal and relevant superpotential couplings at large N (which was previously known only for Nf = 1). In addition, we compute in these theories the 2point and 3point functions of the lowest gaugeinvariant singlet superfield at large N, for all values of lambda and of the superpotential couplings, and use them to test the large N dualities. This computation is one of the ingredients needed for a computation of the beta function at order 1/N for all lambda, which we leave for future work. We also discuss ChernSimonsmatter theories with extra HubbardStratonovich type singlet fields, and suggest dualities between them.

(2019) Journal of High Energy Physics. 2019, 6, 104. Abstract
We consider a string dual of a partially topological U(N) ChernSimonsmatter (PTCSM) theory recently introduced by Aganagic, Costello, McNamara and Vafa. In this theory, fundamental matter fields are coupled to the ChernSimons theory in a way that depends only on a transverse holomorphic structure on a manifold; they are not fully dynamical, but the theory is also not fully topological. One description of this theory arises from topological strings on the deformed conifold TS3 with N Lagrangian 3branes and additional coisotropic flavor' 5branes. Applying the idea of the GopakumarVafa duality to this setup, we suggest that this has a dual description as a topological string on the resolved conifold CP1, in the presence of coisotropic 5branes. We test this duality by computing the annulus amplitude on the deformed conifold and the disc amplitude on the resolved conifold via equivariant localization, and we find an agreement between the two. We find a small discrepancy between the topological string results and the large N limit of the partition function of the PTCSM theory arising from the deformed conifold, computed via field theory localization by a method proposed by Aganagic et al. We discuss possible origins of the mismatch.

(2019) Journal of High Energy Physics. 1, 085. Abstract
We study families of two dimensional quantum field theories, labeled by a dimensionful parameter , that contain a holomorphic conserved U(1) current J(z). We assume that these theories can be consistently defined on a torus, so their partition sum, with a chemical potential for the charge that couples to J, is modular covariant. We further require that in these theories, the energy of a state at finite is a function only of , and of the energy, momentum and charge of the corresponding state at = 0, where the theory becomes conformal. We show that under these conditions, the torus partition sum of the theory at = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in , to be that of a JT deformed conformal field theory (CFT). We derive a flow equation for the J deformed partition sum, and use it to study nonperturbative effects. We find nonperturbative ambiguities for any nonzero value of , and comment on their possible relations to holography.

(2019) Journal of High Energy Physics. 2019, 1, 086. Abstract
Any two dimensional quantum field theory that can be consistently defined on a torus is invariant under modular transformations. In this paper we study families of quantum field theories labeled by a dimensionful parameter t, that have the additional property that the energy of a state at finite t is a function only of t and of the energy and momentum of the corresponding state at t = 0, where the theory becomes conformal. We show that under this requirement, the partition sum of the theory at t = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in t, to be that of a TTdeformed CFT. Nonperturbatively, we find that for one sign of t (for which the energies are real) the partition sum is uniquely determined, while for the other sign we find nonperturbative ambiguities. We characterize these ambiguities and comment on their possible relations to holography.
2018

(2018) Journal of High Energy Physics. 12, 058. Abstract
It has been conjectured that 3d fermions minimally coupled to ChernSimons gauge fields are dual to 3d critical scalars, also minimally coupled to ChernSimons gauge fields. The large N arguments for this duality can formally be used to show that ChernSimonsgauged critical (GrossNeveu) fermions are also dual to gauged regular ' scalars at every order in a 1/N expansion, provided both theories are welldefined (when one finetunes the two relevant parameters of each of these theories to zero). In the strict large N limit these quasibosonic' theories appear as fixed lines parameterized by x(6), the coefficient of a sextic term in the potential. While x(6) is an exactly marginal deformation at leading order in large N, it develops a nontrivial function at first subleading order in 1/N. We demonstrate that the beta function is a cubic polynomial in x(6) at this order in 1/N, and compute the coefficients of the cubic and quadratic terms as a function of the 't Hooft coupling. We conjecture that flows governed by this leading large N beta function have three fixed points for x(6) at every nonzero value of the 't Hooft coupling, implying the existence of three distinct regular bosonic and three distinct dual critical fermionic conformal fixed points, at every value of the 't Hooft coupling. We analyze the phase structure of these fixed point theories at zero temperature. We also construct dual pairs of large N finetuned renormalization group flows from supersymmetric N=2 ChernSimonsmatter theories, such that one of the flows ends up in the IR at a regular boson theory while its dual partner flows to a critical fermion theory. This construction suggests that the duality between these theories persists at finite N, at least when N is large.

(2018) Physical Review Letters. 121, 7, 071601. Abstract
We study the renormalization group flow in general quantum field theories with quenched disorder, focusing on random quantum critical points. We show that in disorderaveraged correlation functions the flow mixes local and nonlocal operators. This leads to a new critical exponent related to the disorder (as in classical disorder). We show that the time coordinate is rescaled at each renormalization group step, leading to anisotropic spacetime scaling at critical points. We write a universal formula for the dynamical scaling exponent z for weak disorder.

(2018) Physical Review D. 98, 4, 045012. Abstract
In this paper, we analyze the renormalization group (RG) flow of field theories with quenched disorder, in which the couplings vary randomly in space. We analyze both classical (Euclidean) disorder and quantum disorder, emphasizing general properties rather than specific cases. The RG flow of the disorderaveraged theories takes place in the space of their coupling constants and also in the space of distributions for the disordered couplings, and the two mix together. We write down a generalization of the CallanSymanzik equation for the flow of disorderaveraged correlation functions. We find that local operators can mix with the response of the theory to local changes in the disorder distribution and that the generalized CallanSymanzik equation mixes the disorder averages of several different correlation functions. For classical disorder, we show that this can lead to new types of anomalous dimensions and to logarithmic behavior at fixed points. For quantum disorder, we find that the RG flow always generates a rescaling of time relative to space, which at a fixed point generically leads to Lifshitz scaling. The dynamical scaling exponent z behaves as an anomalous dimension (as in other nonrelativistic RG flows), and we compute it at leading order in perturbation theory in the disorder for a general theory. Our results agree with a previous perturbative computation by Boyanovsky and Cardy, and with a holographic disorder computation of Hartnoll and Santos. We also find in quantum disorder that local operators mix with nonlocal (in time) operators under the RG, and that there are critical exponents associated with the disorder distribution that have not previously been discussed. In largeN theories, the disorder averages may be computed exactly, and we verify that they are consistent with the generalized CallanSymanzik equations.

(2018) Journal of High Energy Physics. 2018, 8, 166. Abstract
Threedimensional ChernSimons vector models display an approximate higher spin symmetry in the large N limit. Their singletrace operators consist of a tower of weakly broken currents, as well as a scalar a of approximate twist 1 or 2. We study the consequences of crossing symmetry for the fourpoint correlator of a in a 1/N expansion, using analytic bootstrap techniques. To order 1/N we show that crossing symmetry fixes the contribution from the tower of currents, providing an alternative derivation of wellknown results by Maldacena and Zhiboedov. When sigma has twist 1 its OPE receives a contribution from the exchange of a itself with an arbitrary coefficient, due to the existence of a marginal sextic coupling. We develop the machinery to determine the corrections to the OPE data of doubletrace operators due to this, and to similar exchanges. This in turns allows us to fix completely the correlator up to three known truncated solutions to crossing. We then proceed to study the problem to order 1/N2. We find that crossing implies the appearance of oddtwist doubletrace operators, and calculate their OPE coefficients in a large spin expansion. Also, surprisingly, crossing at order 1/N2, implies nontrivial O(1/N) anomalous dimensions for eventwist doubletrace operators, even though such contributions do not appear in the fourpoint function at order 1/N (in the case where there is no scalar exchange). We argue that this phenomenon arises due to operator mixing. Finally, we analyse the bosonic vector model with a sextic coupling without gauge interactions, and determine the order 1/N2 corrections to the dimensions of twist2 doubletrace operators.

(2018) Journal of High Energy Physics. 2018, 5, 166. Abstract
We study Zamolodchikov’s TT¯ deformation of two dimensional quantum field theories in a ’t Hooftlike limit, in which we scale the number of degrees of freedom c to infinity and the deformation parameter t to zero, keeping their product t · c fixed (more precisely, we keep energies and distances fixed in units of t · c). In this limit the Hagedorn temperature remains fixed, but other nonlocal aspects of the theory disappear. We show that in this limit correlation functions may be computed exactly, and they are local in space and polynomials in t. We compute explicitly the deformed threepoint functions of the energymomentum tensor for a TT¯ deformed conformal field theory.
2017

(2017) Journal of High Energy Physics. 2017, 11, 090. Abstract
In this paper we discuss 3d N = 2 supersymmetric gauge theories and their IR dualities when they are compactified on a circle of radius r, and when we take the 2d limit in which r > 0. The 2d limit depends on how the mass parameters are scaled as r > 0, and often vacua become infinitely distant in the 2d limit, leading to a direct sum of different 2d theories. For generic mass parameters, when we take the same limit on both sides of a duality, we obtain 2d dualities (between gauge theories and/or LandauGinzburg theories) that pass all the usual tests. However, when there are noncompact branches the discussion is subtle because the metric on the moduli space, which is not controlled by supersymmetry, plays an important role in the lowenergy dynamics after compactification. Generally speaking, for IR dualities of gauge theories, we conjecture that dualities involving noncompact Higgs branches survive. On the other hand when there is a noncompact Coulomb branch on at least one side of the duality, the duality fails already when the 3d theories are compactified on a circle. Using the valid reductions we reproduce many known 2d IR dualities, giving further evidence for their validity, and we also find new 2d dualities.

(2017) Journal of High Energy Physics. 2017, 7, 036. Abstract
We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to nonplanar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the fourpoint, looplevel Mellin amplitudes can be fully reconstructed from the leadingorder data. The anomalous dimensions computed with both methods agree. In the case of phi(Lambda) theory in AdS, our crossing solution reproduces a previous computation of the oneloop bubble diagram. We can go further, deriving the fourpoint scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an in finite series of poles, and discuss applications to more complicated cases such as the N = 4 superYangMills theory.

(2017) Journal of High Energy Physics. 2017, 2, 056. Abstract
Twodimensional field theories do not have a moduli space of vacua. Instead, it is common that their lowenergy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss twodimensional gauge theories with N = (2, 2) supersymmetry. We focus on two specific theories, for which we argue that they flow to free chiral multiplets at low energies: the U(1) gauge theory with one flavor (two chiral superfields with charges plus and minus one) and a nonzero FayetIliopoulos term, and pure SU(N) gauge theories. We argue that the renormalization group flow of these theories has an interesting order of limits issue. Holding the position on the target space fixed, the space flattens out under the renormalization group. On the other hand, if we first go to infinity on the target space and then perform the renormalization group, we always have a nontrivial space, e.g. a cone with a deficit angle. We explain how to interpret lowenergy dualities between theories with noncompact target spaces. We expect a similar qualitative behavior also for other noncompact sigma models, even when they do not flow to free theories.

(2017) Journal of High Energy Physics. 2017, 2, 072. Abstract
In the last few years several dualities were found between the lowenergy behaviors of ChernSimonsmatter theories with unitary gauge groups coupled to scalars, and similar theories coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between SO(N)(k) ChernSimons theories coupled to Nf real scalars in the fundamental representation, and SO(k)(N+Nf/2) theories coupled to Nf real (Majorana) fermions in the fundamental. For Nf = 0 these are just levelrank dualities of pure ChernSimons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. For k = 1 we get an interesting lowenergy duality between Nf free Majorana fermions and an SO(N)(1) ChernSimons theory coupled to Nf scalar fields (with Nf ≤ N − 2).
2016

(2016) Journal of High Energy Physics. 2016, 6, 044. Abstract
Sfolds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by nontrivial Sduality transformations. They were recently used by GarciaEtxebarria and Regalado to provide the first construction of four dimensional N = 3 superconformal theories. In this note, we classify the different variants of these N = 3preserving Sfolds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification of the Sfolds to three dimensional Mtheory backgrounds. Upon adding D3branes, these variants lead to different classes of N = 3 superconformal field theories. We also analyze the holographic duals of these theories, and in particular clarify the role of discrete gauge and global symmetries in holography.

(2016) Journal of High Energy Physics. 2016, 4, 066. Abstract
In this paper we study supersymmetric field theories on an AdS(p) x Sq spacetime that preserves their full supersymmetry. This is an interesting example of supersymmetry on a noncompact curved space. The supersymmetry algebra on such a space is a (p  1)dimensional superconformal algebra, and we classify all possible algebras that can arise for p >= 3. In some AdS(3) cases more than one superconformal algebra can arise from the same field theory. We discuss in detail the special case of four dimensional field theories with N = 1 and N = 2 supersymmetry on AdS(3) x S1.

(2016) Journal of High Energy Physics. 2016, 4, 013. Abstract
We consider Euclidean Conformal Field Theories perturbed by quenched disorder, namely by random fluctuations in their couplings. Such theories are relevant for secondorder phase transitions in the presence of impurities or other forms of disorder. Theories with quenched disorder often flow to new fixed points of the renormalization group. We begin with disorder in free field theories. Imry and Ma showed that disordered free fields can only exist for d > 4. For d > 4 we show that disorder leads to new fixed points which are not scaleinvariant. We then move on to largeN theories (vector models or gauge theories in the 't Hooft limit). We compute exactly the beta function for the disorder, and the correlation functions of the disordered theory. We generalize the results of Imry and Ma by showing that such disordered theories exist only when disorder couples to operators of dimension Delta > d/4. Sometimes the disordered fixed points are not scaleinvariant, and in other cases they have unconventional dependence on the disorder, including nontrivial effects due to irrelevant operators. Holography maps disorder in conformal theories to stochastic differential equations in a higher dimensional space. We use this dictionary to reproduce our field theory results. We also study the leading 1/N corrections, both by field theory methods and by holography. These corrections are particularly important when disorder scales with the number of degrees of freedom.

(2016) Journal of High Energy Physics. 2016, 4, 040. Abstract
In this note we study four dimensional theories with N = 3 superconformal symmetry, that do not also have N = 4 supersymmetry. No examples of such theories are known, but their existence is also not ruled out. We analyze several properties that such theories must have. We show that their conformal anomalies obey a = c. Using the N = 3 superconformal algebra, we show that they do not have any exactly marginal deformations preserving N = 3 supersymmetry, or global symmetries (except for their Rsymmetries). Finally, we analyze the possible dimensions of chiral operators labeling their moduli space.

(2016) Journal of High Energy Physics. 2, 093. Abstract
There is significant evidence for a duality between (nonsupersymmetric) U(N) ChernSimons theories at level k coupled to fermions, and U(k) ChernSimons theories at level N coupled to scalars. Most of the evidence comes from the large N 't Hooft limit, where many details of the duality (such as whether the gauge group is U(N) or SU(N), the precise level of the U(1) factor, and order one shifts in the level) are not important. The main evidence for the validity of the duality at finite N comes from adding masses and flowing to pure ChernSimons theories related by levelrank duality, and from flowing to the nonsupersymmetric duality from supersymmetric dualities, whose finite N validity is wellestablished. In this note we clarify the implications of these flows for the precise form of the duality; in particular we argue that in its simplest form the duality maps SU(N) theories to U(k) theories, though there is also another version relating U(N) to U(k). This precise form strongly affects the mapping under the duality of baryon and monopole operators, and we show, following arguments by Radicevic, that their mapping is consistent with our claims. We also discuss the implications of our results for the additional duality between these ChernSimons matter theories and (the UV completion of) highspin gravity theories on AdS(4). The latter theories should contain heavy particles carrying electric and/or magnetic charges under their U(1) gauge symmetry.
2015

(2015) Journal of High Energy Physics. 2015, 5, 31. Abstract
Field theories with weakly coupled holographic duals, such as large N gauge theories, have a natural separation of their operators into 'singletrace operators' (dual to singleparticle states) and 'multitrace operators (dual to multiparticle states). There are examples of large N gauge theories where the beta functions of singletrace coupling constants all vanish, but marginal multitrace coupling constants have nonvanishing beta functions that spoil conformal invariance (even when all multitrace coupling constants vanish). The holographic dual of such theories should be a classical solution in antide Sitter space, in which the boundary conditions that correspond to the multitrace coupling constants depend on the cutoff scale, in a way that spoils conformal invariance. We argue that this is realized through specific bulk coupling constants that lead to a running of the multitrace coupling constants. This fills a missing entry in the holographic dictionary.

(2015) Journal of High Energy Physics. 2015, 5, 117. Abstract
We discuss monopole operators in U(Nc) ChernSimonsmatter theories in three spacetime dimensions. We mention an apparent problem in the matching of such operators in dualities between nonsupersymmetric theories, and suggest a possible resolution. A similar apparent problem exists in the mapping of chiral monopole operators in theories with N = 2 supersymmetry. We show that in many theories the lowest naive chiral monopole operator is actually not chiral, and we find the lowest monopole operator that is actually chiral in these theories. It turns out that there are several different forms of this operator, depending on the number of colors, the number of flavours, and the ChernSimons level. Since we use the supersymmetric index to find the lowest chiral monopoles, our results for these monopoles are guaranteed to be invariant under the dualities in supersymmetric theories. The theories we discuss are believed to be dual in the 't Hooft large Nc limit to classical highspin gravity theories. We argue that these theories (supersymmetric or not) should not have classical solutions charged under the U(1) gauge field in the highspin multiplet.

(2015) Journal of High Energy Physics. 2015, 3, 121. Abstract
Field theories on antide Sitter (AdS) space can be studied by realizing them as lowenergy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the sixdimensional N = (2, 0) A(K1) superconformal field theory (SCFT) on AdS(5)xS(1), with equal radii for AdS(5) and for S1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS(5)xS(5)/Z(K). On R(4,1)xS(1), this sixdimensional theory has a 5(K1)dimensional moduli space, with unbroken fivedimensional SU(K) gauge symmetry at (and only at) the origin. On AdS(5)xS(1), the theory has a 2(K1)dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this fivedimensional gauge theory is coupled to a fourdimensional theory on the boundary of AdS(5) whose coupling constants depend on the 'moduli'. This involves nonstandard boundary conditions for the gauge fields on AdS(5). Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled fourdimensional N = 2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the sixdimensional N = (2, 0) theory on AdS(5)xS(1) with sources on the boundary is a subsector of the large N limit of various fourdimensional N = 2 quiver SCFTs that remains nontrivial in the large N limit. The same subsector appears universally in many different fourdimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories’ on AdS5 × S 1.

(2015) Journal of High Energy Physics. 2015, 2, 162. Abstract
In the last twenty years, lowenergy (IR) dualities have been found for many pairs of supersymmetric gauge theories with four supercharges, both in four spacetime dimensions and in three spacetime dimensions. In particular, duals have been found for 3d N = 2 supersymmetric QCD theories with gauge group U(N), with F chiral multiplets in the fundamental representation, with (F) over tilde chiral multiplets in the antifundamental representation, and with ChernSimons level k, for all values of N, F, (F) over tilde and k for which the theory preserves supersymmetry. For SU(N) theories the duals have been found in some cases, such as F = (F) over tilde and (F) over tilde = 0, but not in the general case. In this note we find the IR dual for SU(N) SQCD theories with general values of N, F, (F) over tilde and k not equal 0 which preserve supersymmetry.
2013

(2013) Journal of High Energy Physics. 8, Abstract
We extend recent work on the relation of 4d and 3d IR dualities of supersymmetric gauge theories with four supercharges to the case of orthogonal gauge groups. The distinction between different SO(N) gauge theories in 4d plays an important role in this relation. We show that the 4d duality leads to a 3d duality between an SO(Nc) gauge theory with Nf flavors and an SO(Nf  Nc + 2) theory with Nf flavors and extra singlets, and we derive its generalization in the presence of ChernSimons terms. There are two different O(N) theories in 3d, which we denote by O(N)(+/), and we also show that the O(Nc)gauge theory is dual to a Spin(Nf  Nc + 2) theory, and derive from 4d the known duality between O(Nc)(+) and O(Nf  Nc + 2)(+). We verify the consistency of these 3d dualities by various methods, including index computations.

(2013) Journal of High Energy Physics. 2013, 8, 115. Abstract
Starting with a choice of a gauge group in four dimensions, there is often freedom in the choice of magnetic and dyonic line operators. Different consistent choices of these operators correspond to distinct physical theories, with the same correlation functions of local operators in R4. In some cases these choices are permuted by shifting the thetaangle by 2 pi. In other cases they are labeled by new discrete thetalike parameters. Using this understanding we gain new insight into the dynamics of fourdimensional gauge theories and their phases. The existence of these distinct theories clarifies a number of issues in electric/magnetic dualities of supersynametric gauge theories, both for the conformal N = 4 theories and for the lowenergy dualities of N = 1 theories.

(2013) Journal of High Energy Physics. 7, Abstract
Many examples of lowenergy dualities have been found in supersyrnmetric gauge theories with four supercharges, both in four and in three spacetime dimensions. In these dualities, two theories that are different at high energies have the same lowenergy limit. In tins paper we clarify the relation between the dualities in four and in three dimensions. We show that every four dimensional duality gives rise to a three dimensional duality between theories that are similar, but not identical, to the dimensional reductions of the four dimensional dual gauge theories to three dimensions. From these specific three dimensional dualities one can flow to many other lowenergy dualities, including known three dimensional dualities and many new ones. We discuss in detail the case of three dimensional SU(Nc) supersymmetric QCD theories, showing how to derive new duals for these theories from the four dimensional duality.

(2013) Journal of High Energy Physics. 5, Abstract
We present the lowenergy effective theory on long strings in quantum field theory, including a streamlined review of previous literature on the subject. Such long strings can appear in the form of solitonic strings, as in the 4d Abelian Higgs model, or in the form of confining strings, as in YangMills theories. The bottom line is that upon expanding in powers of 1/L the energy levels of long (closed) strings (where L is the length of the string), all the terms up to (and including) order 1/L5 are universal. We argue that for excited strings in D > 3 spacetime dimensions there is a universal deviation at order 1/L5 from the naive formula that is usually used to fit lattice results. For D = 3 this naive formula is valid even at order 1/L5. At order 1/L7 nonuniversal terms generically appear in all cases. We explain the physical origin of these results, and illuminate them in three different formulations of the effective action of long strings (the relationships among which we partly clarify). In addition, we corroborate these results by an explicit computation of the effective action on long strings in confining theories which have a gravitational dual. These predictions can be tested by precise simulations of 4d YangMills theory on the lattice.

(2013) Journal of High Energy Physics. 2013, 3, Abstract
We compute the thermal free energy in large N U(N) ChernSimonsmatter theories with matter fields (scalars and/or fermions) in the fundamental representation, in the large temperature limit. We note that in these theories the eigenvalue distribution of the holonomy of the gauge field along the thermal circle does not localize even at very high temperatures, and this affects the computation significantly. We verify that our results are consistent with the conjectured dualities between ChernSimonsmatter theories with scalar fields and with fermion fields, as well as with the strongweak coupling duality of the N = 2 supersymmetric ChernSimonsmatter theory.

(2013) Journal of High Energy Physics. 2, Abstract
Four dimensional gauge theories in antide Sitter space, including pure YangMills theory, exhibit a quantum phase transition between a deconfined phase and a confined phase as the gauge coupling is varied. We explore various mechanisms by which this may occur, both in a fixed background and in the presence of gravity. We also make a number of observations on the dynamics of four dimensional supersymmetric gauge theories in antide Sitter space.
2012

(2012) Journal of High Energy Physics. 2012, 12, 28. Abstract
We consider the conformal field theory of N complex massless scalars in 2+1 dimensions, coupled to a U(N) ChernSimons theory at level k. This theory has a 't Hooft large N limit, keeping fixed lambda equivalent to N/k. We compute some correlation functions in this theory exactly as a function of lambda, in the large N (planar) limit. We show that the results match with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have highspin symmetries in the large N limit. It has been suggested in the past that this theory is dual (in the large N limit) to the Legendre transform of the theory of fermions coupled to a ChernSimons gauge field, and our results allow us to find the precise mapping between the two theories. We find that in the large N limit the theory of N scalars coupled to a U(N)(k) ChernSimons theory is equivalent to the Legendre transform of the theory of k fermions coupled to a U(k)(N) ChernSimons theory, thus providing a bosonization of the latter theory. We conjecture that perhaps this duality is valid also for finite values of N and k, where on the fermionic side we should now have (for Nf flavors) a U(k)(NNf/2) theory. Similar results hold for real scalars (fermions) coupled to the O(N)(k) ChernSimons theory.

(2012) Journal of High Energy Physics. 2012, 8, 131. Abstract
We discuss the gravity duals of 4d N = 2 superconformal field theories (SCFTs) arising from the lowenergy limit of brane configurations of D4branes stretched between and intersecting NS5branes and D6branes. This gives rise to a product of SU(Ni) groups, with bifundamental matter between adjacent groups, and extra fundamental hypermultiplets. The most general configuration in 11d (or type IIA) supergravity that is dual to a 4d N = 2 SCFT (when the dual of this SCFT is a weakly curved background) was written down by Gaiotto and Maldacena, but finding it explicitly involves solving a complicated Toda equation. This equation simplifies only when the solution can be reduced to type IIA supergravity, so we ask for which SCFTs of this type is there a type IIA dual that is weakly coupled and weakly curved (away from NS5branes and D6branes). We find that such solutions (a special case of which was analyzed by ReidEdwards and Stefanski) exist when there is a large number of gauge groups, with large ranks, and with large 't Hooft couplings for all but a finite number of groups. The general solution of this type is given by solving an axially symmetric Laplace equation in three dimensions, with specific boundary conditions. We match the parameters of the 4d SCFTs, including the exactly marginal coupling constants, with the boundary conditions for the Laplace equation.

(2012) Journal of High Energy Physics. 2012, 4, 48. Abstract
The lowenergy effective action on long stringlike objects in quantum field theory, such as confining strings, includes the NambuGoto action and then higherderivative corrections. This action is diffeontorphisminvariant, and can be analyzed in various gauges. Polchinski and Strominger suggested a specific way to analyze this effective action in the orthogonal gauge, in which the induced metric on the worldsheet is conformally equivalent to a flat metric. Their suggestion leads to a specific term at the next order beyond the NambuGoto action. We compute the leading correction to the NambuGoto spectrum using the action that includes this term, and we show that it agrees with the leading correction previously computed in the static gauge. This gives a consistency check for the framework of Polchinski and Strominger, and helps to understand its relation to the theory in the static gauge.

(2012) Journal of High Energy Physics. 3, Abstract
We study three dimensional O(N)(k) and U(N)(k) ChernSimons theories coupled to a scalar field in the fundamental representation, in the large N limit. For in finite k this is just the singlet sector of the O (N) (U(N)) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS(4). For large k and N we obtain a paritybreaking deformation of this theory, controlled by the 't Hooft coupling lambda = 4 pi N/k. For infinite N we argue (and show explicitly at twoloop order) that the theories with finite lambda are conformally invariant, and also have an exactly marginal (phi(2))(3) deformation. For large but finite N and small 't Hooft coupling lambda, we show that there is still a line of fixed points parameterized by the 't Hooft coupling lambda. We show that, at in finite N, the interacting nonparityinvariant theory with finite lambda has the same spectrum of primary operators as the free theory, consisting of an in finite tower of conserved higherspin currents and a scalar operator with scaling dimension Delta = 1; however, the correlation functions of these operators do depend on lambda. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by lambda, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.

(2012) Journal of High Energy Physics. 2, Abstract
We study the lowenergy effective action governing the transverse fluctuations of a long string, such as a confining flux tube in QCD. We work in the static gauge where this action contains only the transverse excitations of the string. The static gauge action is strongly constrained by the requirement that the Lorentz symmetry, that is spontaneously broken by the long string vacuum, is nonlinearly realized on the NambuGoldstone bosons. One solution to the constraints (at the classical level) is the NambuGoto action, and the general solution contains higher derivative corrections to this. We show that in 2 + 1 dimensions, the first allowed correction to the NambuGoto action is proportional to the squared curvature of the induced metric on the worldsheet. In higher dimensions, there is a more complicated allowed correction that appears at lower order than the curvature squared. We argue that this leading correction is similar to, but not identical to, the oneloop determinant roothR rectangle R1 computed by Polyakov for the bosonic fundamental string.
2011

(2011) Journal of High Energy Physics. 2011, 12, 043. Abstract
We study three dimensional N = 2 supersymmetric QCD theories with O(Nc) gauge groups and with Nf chiral multiplets in the vector representation. We argue that for Nf = Nc  2 there is a moduli space also in the quantum theory, and for Nf >= Nc  1 there is a superconformal fixed point at the origin of this moduli space that has a dual description as the low energy fixed point of an O(Nf  Nc + 2) gauge theory. We test this duality in various ways; in some cases the duality for an O(2) gauge theory may be related to the known duality for U(1) gauge theories. We also discuss real mass deformations, which allow to connect theories with a different Chern Simons level. This allows us to connect our duality with the known duality in O(Nc) theories with a Chern Simons term of level k, where the dual gauge group is given by O(Nf + vertical bar k vertical bar  Nc + 2).

(2011) Physical Review D. 84, 12, 126003. Abstract
We construct the type IIB supergravity solutions describing D3branes ending on 5branes, in the nearhorizon limit of the D3branes. Our solutions are holographically dual to the four dimensional (4D) N = 4 SU(N) supersymmetricYangMills (SYM) theory on a half line, at large N and large 't Hooft coupling, with various boundary conditions that preserve half of the supersymmetry. The solutions are limiting cases of the general solutions with the same symmetries constructed in 2007 by D'Hoker, Estes and Gutperle. The classification of our solutions matches exactly with the general classification of boundary conditions for D3branes ending on 5branes by Gaiotto and Witten. We use the gravity duals to compute the onepoint functions of some chiral operators in the N = 4 SYM theory on a half line at strong coupling, and we find that they do not match with the expectation values of the same operators with the same boundary conditions at small 't Hooft coupling. Our solutions may also be interpreted as the gravity duals of 4D N = 4 SYM on AdS(4), with various boundary conditions.

(2011) Journal of High Energy Physics. 2, 041. Abstract
In this paper we discuss the dynamics of conformal field theories on antide Sitter space, focussing on the special case of the N = 4 supersymmetric YangMills theory on AdS(4). We argue that the choice of boundary conditions, in particular for the gauge field, has a large effect on the dynamics. For example, for weak coupling, one of two natural choices of boundary conditions for the gauge field leads to a large N deconfinement phase transition as a function of the temperature, while the other does not. For boundary conditions that preserve supersymmetry, the strong coupling dynamics can be analyzed using Sduality (relevant for gYM >> 1), utilizing results of Gaiotto and Witten, as well as by using the AdS/CFT correspondence (relevant for large N and large 't Hooft coupling). We argue that some very specific choices of boundary conditions lead to a simple dual gravitational description for this theory, while for most choices the gravitational dual is not known. In the cases where the gravitational dual is known, we discuss the phase structure at large 't Hooft coupling.

(2011) Journal of High Energy Physics. 2011, 1, 65. Abstract
We study the general lowenergy effective action on long open strings, such as confining strings in pure gauge theories. Using Lorentz invariance, we find that for a string of length R, the leading deviation from the NambuGoto energy levels generically occurs at order 1/R(4) (including a correction to the ground state energy), as opposed to 1/R(5) for excited closed strings in four dimensions, and 1/R(7) for closed strings in three dimensions. This is true both for Dirichlet and for Neumann boundary conditions for the transverse directions, though the worldsheet boundary actions are different. The Dirichlet case is relevant (for instance) for the force between external quarks in a confining gauge theory, and the Neumann case for a string stretched between domain walls. In the specific case of confining gauge theories with a weakly curved holographic dual, we compute the coefficient of the leading correction when the open string ends on two Dbranes, and find a nonvanishing result.
2010

(2010) Journal of High Energy Physics. 12, 58. Abstract
The effective action on long strings, such as confining strings in pure YangMills theories, is wellapproximated by the NambuGoto action, but this action cannot be exact. The leading possible corrections to this action (in a long string expansion in the static gauge), allowed by Lorentz invariance, were recently identified, both for closed strings and for open strings. In this paper we compute explicitly in a Hamiltonian formalism the leading corrections to the lowestlying NambuGoto energy levels in both cases, and verify that they are consistent with the previously computed effective string partition functions. For open strings of length R the leading correction is of order 1/R4, for excited closed strings of length R in D > 3 spacetime dimensions it is of order 1/R5, while for the ground state of the closed string in any dimension it is of order 1/R7. We attempt to match our closed string corrections to lattice results, but the latter are still mostly outside the range of convergence of the 1/R expansion that we use.

(2010) Physical Review D. 82, 10, 106006. Abstract
We study a brane configuration of D4branes and NS5branes in weakly coupled type IIA string theory, which describes in a particular limit d = 4 N =1 SU(N + p) supersymmetric QCD with 2N flavors and a quartic superpotential. We describe the geometric realization of the supersymmetric vacuum structure of this gauge theory. We focus on the confining vacua of the gauge theory, whose holographic description is given by the MQCD brane configuration in the nearhorizon geometry of N D4branes. This description, which gives an embedding of MQCD into a field theory decoupled from gravity, is valid for 1

(2010) Journal of High Energy Physics. 11, 47. Abstract
Understanding the strong coupling limit of massive type IIA string theory is a longstanding problem. We argue that perhaps this problem does not exist; namely, there may be no strongly coupled solutions of the massive theory. We show explicitly that massive type IIA string theory can never be strongly coupled in a weakly curved region of spacetime. We illustrate our general claim with two classes of massive solutions in AdS(4) x CP3: one, previously known, with N = 1 supersymmetry, and a new one with N = 2 supersymmetry. Both solutions are dual to d = 3 ChernSimonsmatter theories. In both these massive examples, as the rank N of the gauge group is increased, the dilaton initially increases in the same way as in the corresponding massless case; before it can reach the Mtheory regime, however, it enters a second regime, in which the dilaton decreases even as N increases. In the N = 2 case, we find supersymmetrypreserving gaugeinvariant monopole operators whose mass is independent of N. This predicts the existence of branes which stay light even when the dilaton decreases. We show that, on the gravity side, these states originate from D2D0 bound states wrapping the vanishing twocycle of a conifold singularity that develops at large N

(2010) Physical Review D. 81, 8, 85006. Abstract
A possible resolution of the flavor puzzle is that the fermion mass hierarchy can be dynamically generated through the coupling of the firsttwogeneration fields to a strongly coupled sector, which is approximately conformally invariant and leads to large anomalous dimensions for the firsttwogeneration fields over a large range of energies. We investigate the possibility of using the same sector to also break supersymmetry. We show that this automatically gives an "inverted hierarchy'' in which the firsttwogeneration squarks and sleptons are much heavier than the other superpartners. Implementing this construction generically requires some finetuning in order to satisfy the constraints on flavorchanging neutral currents at the same time as solving the hierarchy problem. We show that this finetuning can be reduced to be milder than the percent level by making some technically natural assumptions about the form of the strongly coupled sector and its couplings to the standard model.

(2010) Journal of High Energy Physics. 2010, 1, 72. Abstract
We perform a systematic analysis of the Dbrane charges associated with string theory realizations of d = 3 gauge theories, focusing on the examples of the N = 4 supersymmetric U(N) x U(N + M) YangMills theory and the N = 3 supersymmetric U(N) x U(N + M) YangMillsChernSimons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N = 4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N = 3 case, which (for some values of N and M) flows to an N = 6 supersymmetric ChernSimonsmatter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B(2) field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N = 3 theories may exhibit, for some values of N and M, duality cascades similar to those of the KlebanovStrassler theory.
2009

(2009) Journal of High Energy Physics. 6, Abstract
We study the lowenergy effective action on confining strings (in the fundamental representation) in SU(N) gauge theories in D spacetime dimensions. We write this action in terms of the physical transverse fluctuations of the string. We show that for any D, the fourderivative terms in the effective action must exactly match the ones in the NambuGoto action, generalizing a result of Luscher and Weisz for D = 3. We then analyze the sixderivative terms, and we show that some of these terms are constrained. For D = 3 this uniquely determines the effective action for closed strings to this order, while for D > 3 one term is not uniquely determined by our considerations. This implies that for D = 3 the energy levels of a closed string of length L agree with the NambuGoto result at least up to order 1/L(5). For any D we find that the partition function of a long string on a torus is unaffected by the free coefficient, so it is always equal to the NambuGoto partition function up to sixderivative order. For a closed string of length L, this means that for D > 3 its energy can, in principle, deviate from the NambuGoto result at order 1/L(5), but such deviations must always cancel in the computation of the partition function (so that the sum of the deviations of all states at each energy level must vanish). In particular there is no correction at this order to the ground state energy of a winding string. Next, we compute the effective action up to sixderivative order for the special case of confining strings in weaklycurved holographic backgrounds, at oneloop order (leading order in the curvature). Our computation is general, and applies in particular to backgrounds like the Witten background, the MaldacenaNunez background, and the KlebanovStrassler background. We show that this effective action obeys all of the constraints we derive, and in fact it precisely agrees with the NambuGoto action (the single allowed deviation does not appear).
2008

(2008) Journal of High Energy Physics. 2008, 11, 043. Abstract
We consider two generalizations of the N = 6 superconformal ChernSimonsmatter theories with gauge group U(N) x U( N). The first generalization is to N = 6 superconformal U(M) x U(N) theories, and the second to N = 5 superconformal O(2M) x USp(2N) and O(2M + 1) x USp(2N) theories. These theories are conjectured to describe M2branes probing C4/Z(k) in the unitary case, and C4/(D) over cap (k) in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as M  N fractional M2branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals.

(2008) Journal of High Energy Physics. 10, 091. Abstract
We construct three dimensional ChernSimonsmatter theories with gauge groups U(N) x U(N) and SU(N) x SU(N) which have explicit N = 6 superconformal symmetry. Using brane constructions we argue that the U(N) x U(N) theory at level k describes the low energy limit of N M2branes probing a C4/Z(k) singularity. At large N the theory is then dual to Mtheory on AdS(4) x S7/Z(k). The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS(4) x CP3. For k = 1 the theory is conjectured to describe N M2branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) x SU(2) our theory has extra symmetries and becomes identical to the BaggerLambert theory.

NonAbelian structures in compactifications of Mtheory on sevenmanifolds with SU(3) structure(2008) Journal of High Energy Physics. 9, Abstract
We study Mtheory compactified on a specific class of sevendimensional manifolds with SU(3) structure. The manifolds can be viewed as a fibration of an arbitrary CalabiYau threefold over a circle, with a Uduality twist around the circle. In some cases we find that in the four dimensional low energy effective theory a (broken) nonAbelian gauge group appears. Furthermore, such compactifications are shown to be dual to previously analyzed compactifications of the heterotic string on K3 x T2, with background gauge field fluxes on the T2.

(2008) Physical Review D. 78, 2, Abstract
We study the holographic map between long open strings, which stretch between Dbranes separated in the bulk spacetime, and operators in the dual boundary theory. We focus on a generalization of the SakaiSugimoto holographic model of QCD, where the simplest chiral condensate involves an operator of this type. Its expectation value is dominated by a semiclassical string world sheet, as for Wilson loops. We also discuss the deformation of the model by this operator, and, in particular, its effect on the meson spectrum. This deformation can be thought of as a generalization of a quark mass term to strong coupling. It leads to the first topdown holographic model of QCD with a nonAbelian chiral symmetry which is both spontaneously and explicitly broken, as in QCD. Other examples we study include halfsupersymmetric open Wilson lines, and systems of Dbranes ending on NS5branes, which can be analyzed using world sheet methods.

Rho meson condensation at finite isospin chemical potential in a holographic model for QCD(2008) Journal of High Energy Physics. 2, Abstract
We analyze the effect of an isospin chemical potential mu(I) in the SakaiSugimoto model, which is the string dual of a confining gauge theory related to large Nc QCD, at temperatures below the chiral symmetry restoration temperature. For small chemical potentials we show that the results agree with expectations from the lowenergy chiral Lagrangian, and the charged pion condenses. When the chemical potential reaches a critical value mu(I) = mu(crit) similar to 1.7m(p), the lowest vector meson ( the "rho meson") becomes massless, and it condenses ( in addition to the pion condensate) for mu(I) > mu(crit). This spontaneously breaks the rotational symmetry, as well as a residual U( 1) flavor symmetry. We numerically construct the resulting new ground state for mu(I) > mu(crit).

On the conformal field theory duals of type IIA AdS(4) flux compactifications(2008) Journal of High Energy Physics. 2, Abstract
We study the conformal field theory dual of the type IIA flux compactification model of DeWolfe, Giryavets, Kachru and Taylor, with all moduli stabilized. We find its central charge and properties of its operator spectrum. We concentrate on the moduli space of the conformal field theory, which we investigate through domain walls in the type IIA string theory. The moduli space turns out to consist of many different branches. We use Bezout's theorem and Bernstein's theorem to enumerate the different branches of the moduli space and estimate their dimension.

The spacetime operator product expansion in string theory duals of field theories(2008) Journal of High Energy Physics. 1, Abstract
We study the operator product expansion (OPE) limit of correlation functions in field theories which possess string theory duals, from the point of view of the string worldsheet. We show how the interesting ("singletrace") terms in the OPE of the field theory arise in this limit from the OPE of the worldsheet theory of the string dual, using a dominant saddle point which appears in computations of worldsheet correlation functions in the spacetime OPE limit. The worldsheet OPE generically contains only nonphysical operators, but all the nonphysical contributions are resummed by the saddle point to a contribution similar to that of a physical operator, which exactly matches the field theory expectations. We verify that the OPE limit of the worldsheet theory does not have any other contributions to the OPE limit of spacetime correlation functions. Our discussion is completely general and applies to any local field theory (conformal at high energies) that has a weakly coupled string theory dual (with arbitrary curvature). As a first application, we compare our results to a proposal of R. Gopakumar for the string theory dual of free gauge theories.

(2008) Journal of High Energy Physics. 1, Abstract
We use the AdS/CFT correspondence to compute the central charges of the d = 4, N = 2 superconformal field theories arising from N D3branes at singularities in Ftheory. These include the conformal theories with En global symmetries. We compute the central charges a and c related to the conformal anomaly, and also the central charges k associated to the global symmetry in these theories. All of these are related to the coefficients of ChernSimons terms in the dual string theory on AdS(5). Our computation is exact for all values of N, enabling several tests of the dualities recently proposed by Argyres and Seiberg for the E6 and E7 theories with N = 1.
2007

(2007) Physical Review D. 76, 12, Abstract
We present simple string models which dynamically break supersymmetry without nonAbelian gauge dynamics. The Fayet model, the Polonyi model, and the O'Raifeartaigh model each arise from Dbranes at a specific type of singularity. Dbrane instanton effects generate the requisite exponentially small scale of supersymmetry breaking.

(2007) Physical Review D. 76, 8, Abstract
We numerically construct black hole solutions corresponding to the deconfined, chirally symmetric phase of strongly coupled cascading gauge theories at various temperatures. We compute the free energy as a function of the temperature, and we show that it becomes positive below some critical temperature, indicating the possibility of a first order phase transition at which the theory deconfines and restores the chiral symmetry.

Stringy instantons and cascading quivers(2007) Journal of High Energy Physics. 2007, 9, 060. Abstract
Dbrane instantons can perturb the quantum field theories on spacetime filling Dbranes by interesting operators. In some cases, these Dbrane instantons are novel "stringy" effects (not interpretable directly as instanton effects in the lowenergy quantum field theory), while in others the Dbrane instantons can be directly interpreted as field theory effects. In this note, we describe a situation where both perspectives are available, by studying stringy instantons in quivers which arise at simple CalabiYau singularities. We show that a stringy instanton which wraps an unoccupied node of the quiver, and gives rise to a nonperturbative mass in the spacetime field theory, can be reinterpreted as a conventional gauge theory effect by going up in an appropriate renormalization group cascade. Interestingly, in the cascade, the contribution of the stringy instanton does not come from gauge theory instantons but from strong coupling dynamics.

A phase transition in commuting Gaussian multimatrix models(2007) arXiv. Abstract
We analyze in detail a second order phase transition that occurs in large N Gaussian multimatrix models in which the matrices are constrained to be commuting. The phase transition occurs as the relative masses of the matrices are varied, assuming that there are at least four matrices in the lowest mass level. We also discuss the phase structure of weakly coupled large N 3+1 dimensional gauge theories compactified on a threesphere of radius R. We argue that these theories are well described at high temperatures (T >> 1/R) by a Gaussian multimatrix model, and that they do not exhibit any phase transitions between the deconfinement scale (T ~ 1/R) and the scale where perturbation theory breaks down (T ~ 1 / \lambda R, where \lambda is the 't Hooft coupling).

(2007) Annals of Physics. 322, 6, p. 14201443 Abstract
We analyze the finite temperature behavior of the SakaiSugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(Nf)(L) x U(Nf)(R) chiral flavor symmetry at zero temperature. The theory involved is a 4 + 1 dimensional supersymmetric SU(Nc) gauge theory compactified on a circle of radius R with antiperiodic boundary conditions for fermions, coupled to N(f)symmetry is restored at this temperature, but for lefthanded quarks and Nf righthanded quarks which are localized at different points on the compactified on a circle of radius R with antiperiodic boundary conditions for fermions, coupled to Nf lefthanded quarks and Nf righthanded quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large Nc limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature Td = 1/2 pi R. For quark separations obeying L > Lc similar or equal to 0.97 * R the chiral L

(2007) Physical Review D. 75, 10, Abstract
We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in [R. Gopakumar, Phys. Rev. D 70, 025009 (2004); ibid.70, 025010 (2004); C. R. Physique 5, 1111 (2004); Phys. Rev. D 72, 066008 (2005)]. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as deltafunction distributions, and that this can be consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific fourpoint function diagram. To reliably compute this correlator, we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.

The moduli space and M(atrix) theory of 9D N=1 backgrounds of M/string theory(2007) Journal of High Energy Physics. 5, Abstract
We discuss the moduli space of nine dimensional N = 1 supersymmetric compactifications of M theory / string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein bottle and on a Mobius strip, the DabholkarPark Background, CHL strings and asymmetric orbifolds of type II strings on a circle) fit together, and what are the weakly coupled descriptions in different regions of the moduli space. We argue that there are two disconnected components in the moduli space of theories wit hrank 2. We analyze in detail the limits of the M theory compactifications on a Klein bottle and on a Mobius strip which naively give type IIA string theory with an uncharged orientfold 8plane carrying discrete RR flux. In order to consistently describe these limits we conjecture that this orientfold nonperturbatively splits into a D8brane and an orientfold plane of charge (1) which sits at infinite coupling. We construct the M(atrix) theory for M theory on a Klein bottle (and the theories related to it), which is given by a 2 + 1 dimensional gauge theory with a varying gauge coupling compactified on a cylinder with specific boundary conditions. We also clarify the construction of the M(atrix) theory for backgrounds of rank 18, including the heterotic string on a circle.

(2007) Journal of High Energy Physics. 2007, 2, 054. Abstract
Following recent developments in model building we construct a simple, natural and controllable model of gaugemediated supersymmetry breaking.

(2007) Physical Review D. 75, 4, Abstract
Highly supercritical strings (c > 15) with a timelike linear dilaton provide a large class of solutions to string theory, in which closed string tachyon condensation is under control (and follows the world sheet renormalization group flow). In this note we analyze the latetime stability of such backgrounds, including transitions between them. The large friction introduced by the rolling dilaton and the rapid decrease of the string coupling suppress the backreaction of naive instabilities. In particular, although the graviton, dilaton, and other light fields have negative effective mass squared in the linear dilaton background, the decaying string coupling ensures that their condensation does not cause large backreaction. Similarly, the copious particles produced in transitions between highly supercritical theories do not backreact significantly on the solution. We discuss these features also in a somewhat more general class of timedependent backgrounds with stable latetime asymptotics.
2006

Short distance properties of cascading gauge theories(2006) Journal of High Energy Physics. 2006, 11, 069. Abstract
We study the short distance ( large momentum) properties of correlation functions of cascading gauge theories by performing a treelevel computation in their dual gravitational background. We prove that these theories are holographically renormalizable; the correlators have only analytic ultraviolet divergences, which may be removed by appropriate local counterterms. We find that npoint correlation functions of properly normalized operators have the expected scaling in the semiclassical gravity (large N) limit: they scale as Neff(2n) with Neff proportional to ln(k/Lambda) where k is a typical momentum. Our analysis thus confirms the interpretation of the cascading gauge theories as renormalizable fourdimensional quantum field theories with an effective number of degrees of freedom which logarithmically increases with the energy.

(2006) Physical Review D. 74, 10, Abstract
We give a direct pathintegral calculation of the partition function for pure 3+1 dimensional U(N) YangMills theory at large N on a small S3, up to two loop order in perturbation theory. From this, we calculate the one loop shift in the Hagedorn/deconfinement temperature for the theory at small volume, finding that it increases (in units of the inverse sphere radius) as we go to larger coupling (larger volume). Our results also allow us to read off the sum of one loop anomalous dimensions for all operators with a given engineering dimension in planar YangMills theory on R4. As checks on our calculation, we reproduce both the Hagedorn shift and some of the anomalous dimension sums by independent methods using the results of Beisert et al. [Nucl. Phys. B 717, 137 (2005)] and Spradlin and Volovich [Nucl. Phys. B 711, 199 (2005)]. The success of our calculation provides a significant check of methods used by Aharony et al. [Phys. Rev. D 71, 125018 (2005)] to establish a firstorder deconfinement transition for pure YangMills theory on a small S3.

(2006) Physical Review D. 74, 8, Abstract
We discuss the general question of which conformal field theories have dual descriptions in terms of quantum gravity theories on antide Sitter space. We analyze in detail the case of a deformed product of n conformal field theories (each of which has a gravity dual), and we claim that the dual description of this is by a quantum gravity theory on a union of n antide Sitter spaces, connected at their boundary (by correlations between their boundary conditions). On this union of spaces, (n1) linear combinations of gravitons obtain a mass, and we compute this mass both from the field theory and from the gravity sides of the correspondence, finding the same result in both computations. This is the first example in which a graviton mass in the bulk of antide Sitter space arises continuously by varying parameters. The analysis of these deformed product theories leads us to suggest that field theories may be generally classified by a "connectivity index," corresponding to the number of components (connected at the boundary) in the spacetime of the dual gravitational background. In the field theory this index roughly counts the number of independent gauge groups, but we do not have a precise general formula for the index.

On the worldsheet theories of strings dual to free large N gauge theories(2006) Journal of High Energy Physics. 5, Abstract
We analyze in detail some properties of the worldsheet of the closed string theories suggested by Gopakumar to be dual to free large N SU( N) gauge theories (with adjoint matter fields). We use Gopakumar's prescription to translate the computation of space time correlation functions to worldsheet correlation functions for several classes of Feynman diagrams, by explicit computations of Strebel differentials. We compute the worldsheet operator product expansion in several cases and find that it is consistent with general worldsheet conformal field theory expectations. A peculiar property of the construction is that in several cases the resulting worldsheet correlation functions are nonvanishing only on a subspace of the moduli space (say, for specific relations between vertex positions). Another strange property we find is that for a conformally invariant space time theory, the mapping to the worldsheet does not preserve the special conformal symmetries, so that the full conformal group is not realized as a global symmetry on the worldsheet ( even though it is, by construction, a symmetry of all integrated correlation functions).

(2006) Classical and Quantum Gravity. 23, 7, p. 21712210 Abstract
We argue for the existence of plasma ballsmetastable, nearly homogeneous lumps of gluon plasma at just above the deconfinement energy densityin a class of largeN confining gauge theories that undergo firstorder deconfinement transitions. Plasma balls decay over a time scale of order N2 by thermally radiating hadrons at the deconfinement temperature. In gauge theories that have a dual description that is well approximated by a theory of gravity in a warped geometry, we propose that plasma balls map to a family of classically stable finiteenergy black holes localized in the IR. We present a conjecture for the qualitative nature of largemass black holes in such backgrounds and numerically construct these black holes in a particular class of warped geometries. These black holes have novel properties; in particular, their temperature approaches a nonzero constant value at large mass. Black holes dual to plasma balls shrink as they decay by Hawking radiation; towards the end of this process, they resemble tendimensional Schwarzschild black holes, which we propose are dual to small plasma balls. Our work may find practical applications in the study of the physics of localized black holes from a dual viewpoint.

The phase structure of low dimensional large N gauge theories on tori(2006) Journal of High Energy Physics. 1, Abstract
In this paper we continue our study of the thermodynamics of large N gauge theories on compact spaces. We consider toroidal compactifications of pure SU(N) YangMills theories and of maximally supersymmetric YangMills theories dimensionally reduced to 0 + 1 or 1 + 1 dimensions, and generalizations of such theories where the adjoint fields are massive. We describe the phase structure of these theories as a function of the gauge coupling, the geometry of the compact space and the mass parameters. In particular, we study the behavior of order parameters associated with the holonomy of the gauge field around the cycles of the torus. Our methods combine analytic analysis, numerical Monte Carlo simulations, and (in the maximally supersymmetric case) information from the dual gravitational theories.
2005

The conformal limit of the 0A matrix model and string theory on AdS(2)(2005) Journal of High Energy Physics. 11, Abstract
We analyze the conformal limit of the matrix model describing flux backgrounds of two dimensional type0A string theory. This limit is believed to be dual to an AdS(2) background of type0A string theory. We show that the spectrum of this limit is identical to that of a free fermion on AdS(2), suggesting that there are no closed string excitations in this background.

(2005) Physical Review D. 72, 10, Abstract
In the KachruKalloshLindeTrivedi (KKLT) deSitter construction one introduces an antiD3brane that breaks the supersymmetry and leads to a positive cosmological constant. In this paper we investigate the open string moduli associated with this antiD3brane, corresponding to its position on the S3 at the tip of the deformed conifold. We show that in the KKLT construction these moduli are very light, and we suggest a possible way to give these moduli a large mass by putting orientifold planes in the KKLT "throat."

(2005) Journal of High Energy Physics. 2005, 10, 097. Abstract
The AdS/CFT correspondence relates deformations of the CFT by "multitrace operators" to "nonlocal string theories". The deformed theories seem to have nonlocal interactions in the compact directions of spacetime; in the gravity approximation the deformed theories involve modified boundary conditions on the fields which are explicitly nonlocal in the compact directions. In this note we exhibit a particular nonlocal property of the resulting spacetime theory. We show that in the usual backgrounds appearing in the AdS/CFT correspondence, the commutator of two bulk scalar fields at points with a large enough distance between them in the compact directions and a small enough timelike distance between them in AdS vanishes, but this is not always true in the deformed theories. We discuss how this is consistent with causality.

(2005) Physical Review D. 72, 6, Abstract
We perform a holographic renormalization of cascading gauge theories. Specifically, we find the counterterms that need to be added to the gravitational action of the backgrounds dual to the cascading theory of Klebanov and Tseytlin, compactified on an arbitrary fourmanifold, in order to obtain finite correlation functions (with a limited set of sources). We show that it is possible to truncate the action for deformations of this background to a fivedimensional system coupling together the metric and four scalar fields. Somewhat surprisingly, despite the fact that these theories involve an infinite number of highenergy degrees of freedom, we find finite answers for all onepoint functions (including the conformal anomaly). We compute explicitly the renormalized stress tensor for the cascading gauge theories at high temperature and show how our finite answers are consistent with the infinite number of degrees of freedom. Finally, we discuss ambiguities appearing in the holographic renormalization we propose for the cascading gauge theories; our finite results for the onepoint functions have some ambiguities in curved space (including the conformal anomaly) but not in flat space.

(2005) Physical Review D. 71, 12, Abstract
We give an analytic demonstration that the 3+1dimensional large N SU(N) pure YangMills theory, compactified on a small S3 so that the coupling constant at the compactification scale is very small, has a first order deconfinement transition as a function of temperature. We do this by explicitly computing the relevant terms in the canonical partition function up to threeloop order; this is necessary because the leading (oneloop) result for the phase transition is precisely on the border line between a first order and a second order transition. Since numerical work strongly suggests that the infinitevolume large N theory also has a first order deconfinement transition, we conjecture that the phase structure is independent of the size of the S3. To deal with divergences in our calculations, we are led to introduce a novel method of regularization useful for nonAbelian gauge theory on S3.
2004

(2004) Comptes Rendus Physique. 5, 10Sep, p. 945954 Abstract
We demonstrate that weakly coupled, large N, ddimensional SU(N) gauge theories on a class of compact spatial manifolds (including Sd1 x time) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order N2. These phases are separated either by a single first order transition that generically occurs below the Hagedom temperature or by two continuous phase transitions, the first of which occurs at the Hagedorn temperature. These phase transitions appear to be continuously connected to the usual flat space deconfinement transition in the case of confining gauge theories, and to the HawkingPage nucleation of AdS(5) black holes in the case of the N = 4 supersymmetric YangMills theory. Our analysis proceeds by first reducing the YangMills partition function to a (0 + 0)dimensional integral over a unitary matrix U, which is the holonomy (Wilson loop) of the gauge field around the thermal time circle in Euclidean space; deconfinement transitions are large N transitions in this matrix integral. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.

(2004) Classical and Quantum Gravity. 21, 22, p. 51695191 Abstract
We review and extend earlier work that uses the AdS/CFT correspondence to relate the blackholeblackstring transition of gravitational theories on a circle to a phase transition in maximally supersymmetric (1 + 1)dimensional SU(N) 4, Gauge theories at large N, again compactified on a circle. We perform gravity calculations to determine a likely phase diagram for the strongly coupled gauge theory. We then directly study the phase structure of the same gauge theory, now at weak 't Hooft coupling. In the interesting temperature regime for the phase transition, the (1 + 1)dimensional theory reduces to a (0 + 1)dimensional bosonic theory, which we solve using Monte Carlo methods. We find strong evidence that the weakly coupled gauge theory also exhibits a black holeblack stringlike phase transition in the large N limit. We demonstrate that a simple LandauGinzburglike model describes the behaviour near the phase transition remarkably well. The weak coupling transition appears to be close to the cusp between a firstorder and a secondorder transition.

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories(2004) Advances in Theoretical and Mathematical Physics. 8, 4, p. 603696 Abstract
We demonstrate that weakly coupled, large N, ddimensional SU(N) gauge theories on a class of compact spatial manifolds (including Sd1 x time) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order N2. These phases are separated either by a single first order transition that generically occurs below the Hagedorn temperature or by two continuous phase transitions, the first of which occurs at the Hagedorn temperature. These phase transitions could perhaps be continuously connected to the usual flat space deconfinement transition in the case of confining gauge theories, and to the HawkingPage nucleation of AdS(5) black holes in the case of the N = 4 supersymmetric YangMills theory. We suggest that deconfinement transitions may generally be interpreted in terms of black hole formation in a dual string theory. Our analysis proceeds by first reducing the YangMills partition function to a (0 + 0)dimensional integral over a unitary matrix U, which is the holonomy (Wilson loop) of the gauge field around the thermal time circle in Euclidean space; deconfinement transitions are large N transitions in this matrix integral.

(2004) Nuclear Physics B. 691, 2Jan, p. 378 Abstract
We discuss the analytic structure of offshell correlation functions in Little String Theories (LSTs) using their description as asymptotically linear dilaton backgrounds of string theory. We focus on specific points in the LST moduli space where this description involves the spacetime Rd1,R1 x SL(2)/U(1) times a compact CFT, though we expect our qualitative results to be much more general. We show that npoint functions of vertex operators O(pmu) have single poles as a function of the ddimensional momentum pmu, which correspond to normalizable states localized near the tip of the SL(2)/U(1) cigar. Additional poles arise due to the nontrivial dynamics in the bulk of the cigar, and these can lead to a type of UV/IR mixing. Our results explain some previously puzzling features of the low energy behavior of the Green functions. As another application, we compute the precise combinations of singletrace and multitrace operators in the lowenergy gauge theory which map to single string vertex operators in the N = (1, 1) supersymmetric d = 6 LST. We also discuss the implications of our results for twodimensional string theories and for the (nonexistence of a) Hagedorn phase transition in LSTs. (C) 2004 Published by Elsevier B.V.

(2004) Nuclear Physics B. 679, 2Jan, p. 365 Abstract
Little string theory (LST) is a still somewhat mysterious theory that describes the dynamics near a certain class of timelike singularities in string theory. In this paper we discuss the topological version of LST, which describes topological strings near these singularities. For (5 + 1)dimensional LSTs with sixteen supercharges, the topological version may be described holographically in terms of the N = 4 topological string (or the N = 2 string) on the transverse part of the nearhorizon geometry of NS5braves. We show that this topological string can be used to efficiently compute the halfBPS F4 terms in the lowenergy effective action of the LST. Using the strongweak coupling string duality relating type IIA strings on K3 and heterotic strings on T4, the same terms may also be computed in the heterotic string near a point of enhanced gauge symmetry. We study the F4 terms in the heterotic string and in the LST, and show that they have the same structure, and that they agree in the cases for which we compute both of them. We also clarify some additional issues, such as the definition and role of normalizable modes in holographic linear dilaton backgrounds, the precise identifications of vertex operators in these backgrounds with states and operators in the supersymmetric YangMills theory that arises in the low energy limit of LST, and the normalization of twopoint functions. (C) 2003 Elsevier B.V. All rights reserved.

(2004) Lie Theory And Its Applications In Physics V, Proceedings. p. 161203 Abstract
We demonstrate that weakly coupled, large N, ddimensional SU(N) gauge theories on a class of compact spatial manifolds (including Sd1 X time) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order N2. These phases are separated either by a single first order transition that generically occurs below the Hagedorn temperature or by two continuous phase transitions, the first of which occurs at the Hagedorn temperature. These phase transitions may be continuously connected to the usual flat space deconfinement transition in the case of confining gauge theories, and to the HawkingPage nucleation of AdS(5) black holes in the case of the N = 4 supersymmetric YangMills theory. We suggest that deconfinement transitions may generally be interpreted in terms of black hole formation in a dual string theory. Our analysis proceeds by first reducing the YangMills partition function to a (0 + 0)dimensional integral over a unitary matrix U, which is the holonomy (Wilson loop) of the gauge field around the thermal time circle in Euclidean space; deconfinement transitions are large N transitions in this matrix integral.
2003

Defect conformal field theory and locally localized gravity(2003) Journal of High Energy Physics. 7, Abstract
Gravity may be "locally localized" over a wide range of length scales on a ddimensional antide Sitter (AdS) brane living inside AdS(d+l). In this paper we examine this phenomenon from the point of view of the holographic dual "defect conformal field theory". The mode expansion of bulk fields on the gravity side is shown to be precisely dual to the "boundary operator product expansion" of operators as they approach the defect. From the field theory point of view, the condition for localization is that a "reduced operator" appearing in this expansion acquires negative anomalous dimension. In particular, a very light localized graviton exists when a mode arising from the reduction of the ambient stressenergy tensor to the defect has conformal dimension Deltasimilar tod1. The part of the stress tensor containing the defect dynamics has dimension Delta=d1 in the free theory, but we argue that it acquires a positive anomalous dimension in the interacting theory, and does not participate in localization in the regime of small backreaction of the brane. We demonstrate that such an anomalous dimension is consistent with the conservation of the full stressenergy tensor. Finally, we analyze how to compute the anomalous dimensions of reduced operators from gravity at leading order in the interactions with the brane.

The nonAdS/nonCFT correspondence, or three different paths to QCD(2003) Progress In String, Field And Particle Theory. 104, p. 324 Abstract
In these lecture notes from the 2002 Cargese summer school we review the progress that has been made towards finding a string theory for QCD (or for pure (super)YangMills theory) following the discovery of the AdS/CFT correspondence. We start with a brief review of the AdS/CFT correspondence and a general discussion of its application to the construction of a string theory for QCD. We then discuss in detail two possible paths towards a QCD string theory, one which uses a mass deformation of the N = 4 super YangMills theory (the PolchinskiStrassler background) and the other using a compactification of "little string theory" on S2 (the MaldacenaNufiez solution). A third approach (the KlebanovStrassler solution) is described in other lectures of this school. We briefly assess the advantages and disadvantages of all three approaches.
2002

'Holey sheets'  pfaffians and subdeterminants as Dbrane operators in largeN gauge theories(2002) Journal of High Energy Physics. 12, Abstract
In the AdS/CFT correspondence, wrapped D3branes (such as "giant gravitons") on the string theory side of the correspondence have been identified with pfaffian, determinant and subdeterminant operators on the field theory side. We substantiate this identification by showing that the presence of pairs of such operators in a correlation function of a largeN gauge theory naturally leads to a modified 't Hooft expansion including also worldsheets with boundaries. This happens independently of supersymmetry or conformal invariance.

Clean timedependent string backgrounds from bubble baths(2002) Journal of High Energy Physics. 7, Abstract
We consider the set of controlled timedependent backgrounds of general relativity and string theory describing bubbles of nothing, obtained via double analytic continuation of black hole solutions. We analyze their quantum stability, uncover some novel features of their dynamics, identify their causal structure and observables, and compute their particle production spectrum. We present a general relation between squeezed states, such as those arising in cosmological particle creation, and nonlocal theories on the string worldsheet. The bubble backgrounds have various aspects in common with de Sitter space, Rindler space, and moving mirror systems, but constitute controlled solutions of general relativity and string theory with no external forces. They provide a useful theoretical laboratory for studying issues of observables in systems with cosmological horizons, particle creation, and timedependent string perturbation theory.

On exactly marginal deformations of N=4 SYM and typeIIB supergravity on AdS(5) x S5(2002) Journal of High Energy Physics. 2002, 6, 039. Abstract
N = 4 supersymmetric YangMills theory with gauge group SU(N) (N greater than or equal to 3) is believed to have two exactly marginal deformations which break the supersymmetry to N = 1. We discuss the construction of the string theory dual to these deformations, in the supergravity approximation, in a perturbation series around the AdS(5) x S5 solution. We construct explicitly the deformed solution at second order in the deformation. We show that deformations which are marginal but not exactly marginal lead to a nonconformal solution with a logarithmically running coupling constant. Surprisingly, at third order in the deformation we find the same beta functions for the couplings in field theory and in supergravity, suggesting that the leading order beta functions (or anomalous dimensions) do not depend on the gauge coupling (the coefficient is not renormalized)

(2002) Physical review D. 65, 10, Abstract
We exhibit a simple class of exactly marginal "doubletrace" deformations of twodimensional conformal field theories (CFTs) which have AdS(3) duals, in which the deformation is given by a product of left and rightmoving U(1) currents. In this special case the deformation on AdS(3) is generated by a local boundary term in three dimensions, which changes the physics also in the bulk via bulkboundary propagators. However, the deformation is nonlocal in six dimensions and on the string world sheet, as in generic nonlocal string theories. Because of the simplicity of the deformation we can explicitly make computations in the nonlocal string theory and compare them to CFT computations, and we obtain precise agreement. We discuss the effect of the deformation on closed strings and on D branes. The examples we analyze include a supersymmetrybreaking but exactly marginal "doubletrace" deformation, which is dual to a string theory in which no destabilizing tadpoles are generated for moduli nonperturbatively in all couplings, despite the absence of supersymmetry. We explain how this cancellation works on the gravity side in string perturbation theory, and also nonperturbatively at leading order in the deformation parameter. We also discuss possible flat space limits of our construction.

Exactly marginal deformations of N=4 SYM and of its supersymmetric orbifold descendants(2002) Journal of High Energy Physics. 5, Abstract
In this paper we study exactly marginal deformations of field theories living on D3branes at low energies. These theories include N = 4 supersymmetric YangMills theory and theories obtained from it via the orbifolding procedure. We restrict ourselves only to orbifolds and deformations which leave some supersymmetry unbroken. A number of new families of N = 1 superconformal field theories are found. We analyze the deformations perturbatively, and also by using general arguments for the dimension of the space of exactly marginal deformations. We find some cases where the space of perturbative exactly marginal deformations is smaller than the prediction of the general analysis (at least up to threeloop order), and other cases where the perturbative result (at low orders) has a nongeneric form.

Stable nonsupersymmetric supergravity solutions from deformations of the MaldacenaNunez background(2002) Journal of High Energy Physics. 4, Abstract
We study a deformation of the type IIB MaldacenaNunez background which arises as the nearhorizon limit of NS5 branes wrapped on a twocycle. This background is dual to a "little string theory" compactified on a twosphere, a theory which at low energies includes fourdimensional N = 1 super YangMills theory. The deformation we study corresponds to a mass term for some of the scalar fields in this theory, and it breaks supersymmetry completely. In the language of sevendimensional SO(4) gauged supergravity the deformation involves (at leading order) giving a VEV, depending only on the radial coordinate, to a particular scalar field. We explicitly construct the corresponding solution at leading order in the deformation, both in sevendimensional and in tendimensional supergravity, and we verify that it completely breaks supersymmetry. Since the original background had a mass gap and we are performing a small deformation, the deformed background is guaranteed to be stable even though it is not supersymmetric.
2001

Multipletrace operators and nonlocal string theories(2001) Journal of High Energy Physics. 8, Abstract
We propose that a novel deformation of string perturbation theory, involving nonlocal interactions between strings, is required to describe the gravity duals of field theories deformed by multipletrace operators. The new perturbative expansion involves a new parameter, which is neither the string coupling nor the coefficient of a vertex operator on the worldsheet. We explore some of the properties of this deformation, focusing on a special case where the deformation in the field theory is exactly marginal.

(2001) Journal of High Energy Physics. 2001, 3, 12. Abstract
We discuss the field theory interpretation (via holographic duality) of some recentlydiscovered string theory solutions with varying flux, focusing on fourdimensional theories with N = 2 supersymmetry and with N = 1 supersymmetry which arise as the nearhorizon limits of "fractional D3branes". We argue that in the N = 2 case the best interpretation of the varying flux in field theory is via a Higgs mechanism reducing the rank of the gauge group, and that there is no need to invoke a duality to explain the varying flux in this case. We discuss why a similar interpretation does not seem to apply to the N = 1 case of Klebanov and Strassler, which was interpreted as a "duality cascade". However, we suggest that it might apply to different vacua of the same theory, such as the one constructed by Pando Zayas and Tseytlin.