Publications
2018
-
(2018) Journal of High Energy Physics. 2018, 12, 58. Abstract
It has been conjectured that 3d fermions minimally coupled to Chern-Simons gauge fields are dual to 3d critical scalars, also minimally coupled to Chern-Simons gauge fields. The large N arguments for this duality can formally be used to show that Chern-Simons-gauged critical (Gross-Neveu) fermions are also dual to gauged regular scalars at every order in a 1/N expansion, provided both theories are well-defined (when one fine-tunes the two relevant parameters of each of these theories to zero). In the strict large N limit these quasi-bosonic theories appear as fixed lines parameterized by x6, the coefficient of a sextic term in the potential. While x6 is an exactly marginal deformation at leading order in large N, it develops a non-trivial β function at first subleading order in 1/N. We demonstrate that the beta function is a cubic polynomial in x6 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 x6 at every non-zero 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 fine-tuned renormalization group flows from supersymmetric N= 2 Chern-Simons-matter 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) Journal of High Energy Physics. 2018, 8, 166. Abstract
Three-dimensional Chern-Simons vector models display an approximate higher spin symmetry in the large N limit. Their single-trace operators consist of a tower of weakly broken currents, as well as a scalar σ of approximate twist 1 or 2. We study the consequences of crossing symmetry for the four-point correlator of σ 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 well-known results by Maldacena and Zhiboedov. When σ has twist 1 its OPE receives a contribution from the exchange of σ 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 double-trace 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 odd-twist double-trace operators, and calculate their OPE coefficients in a large spin expansion. Also, surprisingly, crossing at order 1/N2, implies non-trivial O(1/N) anomalous dimensions for even-twist double-trace operators, even though such contributions do not appear in the four-point 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 twist-2 double-trace operators.
-
(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 disorder-averaged 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 Callan-Symanzik equation for the flow of disorder-averaged 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 Callan-Symanzik 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 large-N theories, the disorder averages may be computed exactly, and we verify that they are consistent with the generalized Callan-Symanzik equations.
-
(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 disorder-averaged 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) Journal of High Energy Physics. 2018, 5, 166. Abstract
We study Zamolodchikovs TT¯ deformation of two dimensional quantum field theories in a t Hooft-like 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 non-local 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 three-point functions of the energy-momentum tensor for a TT¯ -deformed conformal field theory.