Research
Quantum Gravity, Quantum Chaos and Quantum Information
Quantum Gravity, Quantum Chaos and Quantum information are closely related to each other. In the group we are focusing on the Quantum Chaos and Black holes interface, both for the purposes of the interface and for Quantum Chaos on its own right. We focus on solveable models with rich algebraic structgure, such as the double scaled SYK model, to obtain detailed information about both sides of the Gravity/gauge theory duality. On the gravity side, we would like to obtain more refined information about the structure of spacetime at the Planck scale and its algebraic structure, and on the Quantum Chaotic side we would like to understand new universal properties in Quantum Chaotic systems and how they relate to different ways of taking the large N limit,
Quantum field theories in higher dimensions
Weakly coupled interacting quantum field theories exist only in four or less space-time dimensions. However, there are arguments that consistent quantum field theories exist also in five and six space-time dimensions. In particular there are indirect arguments for the existence of local superconformal field theories in five and six dimensions, and of non-local field theories (called "little string theories") in six dimensions. Can we provide direct constructions of these higher dimensional theories, and understand their properties ? What can we learn about lower dimensional field theories by compactifying these theories on various manifolds ? Are there any consistent field theories above six space-time dimensions, and are there any consistent non-supersymmetric field theories above four space-time dimensions ? What are the rules for dealing with non-local (but non-gravitational) theories like "little string theories" ?
Chaotic Quantum Field Theories
There issue of Quantum Chaos in 1+1 field theories and higher dimensions (in the continuum) is a relatively new territory. Even basic characterizations of Chaotic field theories, or Chaotic conformal field theories, are not clear. There are few tools from gravity, and there are very few computable examples, or computational tools, on the field theory side. Research in the group focuses in pushing this envelope, mainly on the field theory side by 1) Developing new way to characterize and compute Quantum Chaos in existing example, 2) Developing systematic ways of obtaining more examples, and in particular ones closer to having a gravitational dual, 3) Understaing Quantum Chaos in know AdS/CFT high dimensional examples. The goal is both to study specific theories, and develop tools to deals with ensembles of theories (particularlt CFTs) at the same time.
Dualities in quantum field theory
Quantum field theories can easily be studied in perturbation theory when they are weakly coupled, but very little is known about them when they are strongly coupled, even though many interesting field theories (including quantum chromodynamics at low energies) are strongly coupled. For some quantum field theories, it has been found that the strongly coupled theory has an alternative description in terms of some different quantum field theory, that is sometimes weakly coupled. In two space-time dimensions this phenomenon has been known for a long time and is reasonably well-understood. In higher dimensions we have a list of examples of this phenomenon, mostly in supersymmetric field theories, but no general understanding of when and how it happens. Can we find dual descriptions for more strongly coupled field theories in three and four space-time dimensions, in particular for more non-supersymmetric theories ? Can we relate the dualities of different theories (including theories in different space-time dimensions) ? Can we understand duality mappings in general, and obtain rules that will tell us when some theory has a dual description, and what it is ?
String theory and gauge/gravity duality
String theory is a consistent theory of quantum gravity - the only one known so far. However, so far we only have a non-perturbative formulation of this theory on a limited class of space-times which have specific types of boundaries, using the gauge/gravity duality and its generalizations. And even this duality has not yet been derived (though there is substantial evidence that it is true). Can we generalize the gauge/gravity duality to more general situations, for instance to weakly coupled field theories which should be dual to backgrounds with light high-spin fields ("high-spin gravities") ? Can this help us to derive the gauge/gravity duality, namely construct the mapping between the field theory degrees of freedom and those of the gravitational theory (such as string theory) ? Can we find a non-perturbative formulation for string theory on more general backgrounds, such as flat space or de Sitter space ?
On general grounds, we expect some string theory to be dual to every gauge theory (which should become weakly coupled in the large N limit), but so far we only know a very limited number of examples. We are working on understanding the string dual of two dimensional QCD, with the hope of eventually extending this to other two dimensional gauge theories, and finally to higher dimensional theories like four dimensional QCD.
Conformal field theory
Some of the most interesting Quantum Field Theories are conformal. What makes Conformal Field Theories (CFTs) interesting is that they describe second order phase transitions, they are the end-points of renormalization group flows, and they also describe quantum gravity in Anti-de Sitter spaces. A better understanding of CFTs would thus shed light on many interesting branches of physics, ranging from statistical physics to quantum gravity. CFTs above two space-time dimensions remain elusive, and the full power of the conformal group is not yet fully appreciated. In which dimensions do non-trivial CFTs exist ? What can be said about critical exponents at second-order phase transitions ? What can we learn from CFTs about quantum gravity ? Which CFTs can be connected by Renormalization Group flows ? Is the field theory which describes boiling water at the second order phase transition solvable? Some field theories like QCD flow to conformal field theories for some range of their parameters (e.g. the number of flavors) but not for other ranges, how does this "conformal window" end ?