This series consists of talks in the area of Superstring Theory.
We explain how to obtain the spectrum of operators with protected scaling dimensions in a four-dimensional superconformal field theory from cyclic homology. Additionally, we show that the superconformal index of a quiver gauge theory equals the Euler characteristic of the cyclic homology of the Ginzburg dg algebra associated to the quiver. For quiver gauge theories which are dual to type IIB string theory on the product of an arbitrary smooth Sasaki-Einstein manifold with five-dimensional AdS space, the index is calculated both from the gauge theory and gravity viewpoints.
We report on recent advances in understanding the non-local symmetries of quantum field theory, notably gauge theory. The symmetries relate topologically distinct sectors of the field space. We study these symmetries in some detail in the context of the BPS/CFT correspondence. We also introduce a notion of qq-characters, which generalize the q-characters of quantum affine algebras, introduced by E. Frenkel and N. Reshetikhin, and conjecturally are related to the (q, t)-characters introduced by H. Nakajima.
We study the dimensional reduction of 3d QFTs with N=2 supersymmetry. In particular, we are interested in deriving dualities between 2d N=(2,2) theories starting from 3d dualities. Our main tool is the supersymmetric index, ie, the partition function on S^2 x S^1, which formally reduces to the partition function on S^2 as the radius of the circle goes to zero. There are various technical subtleties in this limit of the index which reflect physical subtleties in the reduction of the theories.
Modular invariance plays an important role in the AdS3/CFT2 correspondence. Using modular invariance, I discuss under what conditions a 2d CFT shows a Hawking-Page phase transition in the large c limit, and what this implies for the range of validity of the Cardy formula and the universality of its spectrum. I will also discuss partition functions obtained by summing over the modular group, how their properties are compatible with their gravity interpretation, and briefly touch on implications for the existence of pure gravity.
I will review various aspects of field theories that posses a Lifshitz scaling symmetry. I will detail our study of the cohomological structure of anisotropic Weyl anomalies (the equivalent of trace anomalies in relativistic scale invariant field theories). I will also analyze the hydrodynamics of Lifshitz field theories and in particular of Lifshitz superfluids which may give insights into the physics of high temperature superconductors.
We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. We explore the resulting chiral algebras in the context of theories of class S. The class S duality web implies nontrivial associativity properties for the corresponding chiral algebras, the structure of which can be summarized by a generalized topological quantum field theory.
At large N, an important sector of the ABJM field theory defined on a stack of N M2-branes can be described holographically by the D=4 N=8 SO(8)-gauged supergravity of de Wit and Nicolai. Since its inception, the latter has been tacitly assumed to be unique. Recently, however, a one-parameter family of SO(8) gaugings of N=8 supergravity has been discovered, the de Wit-Nicolai theory being just a member in this class. I will explain how this overlooked family of SO(8)-gauged supergravities is deeply related to electric/magnetic duality breaking in four dimensions.
We construct the gravity duals of large N supersymmetric gauge theories on a squashed five-sphere. They are constructed in Euclidean Romans F(4) gauged supergravity in six-dimensions. We find a one- as well as a two-parameter family of solutions and evaluate the renormalised on-shell and fundamental string action for these solutions to find precise agreement with gauge theory.
We provide a framework for describing gravity duals of four-dimensional N=1 superconformal field theories obtained by compactifying a stack of M5-branes on a Riemann surface. The gravity solutions are completely specified by two scalar potentials whose pole structures on the Riemann surface correspond to the spectrum of punctures that labels different theories. We discuss how to identify these puncture in gravity.