This series consists of talks in the area of Superstring Theory.
I will present recent results on the computation of finite N corrections in supergravity in the context of AdS2/CFT1 and AdS4/ABJM holography. I will show how to use localisation in supergravity to compute all perturbative and nonperturbative charge corrections to the entropy of supersymmetric black holes including complicated number theoretic objects called Kloosterman sums. These are essential to recover an integer which can be identified as the number of black hole ground states.
We discuss a topological description of the confining phase of (Super-)Yang-Mills theories with gauge group SU(N) which encodes all the Aharonov-Bohm phases of configurations of non-local operators. This topological action shows an additional 1-form gauge symmetry. After the introduction of domain walls, this 1-form gauge symmetry demands the appearance of new fields on the worldvolume of the wall. These new fields have a topological Chern-Simons action at level N, also suggested by string theory constructions.
We present integral equations for the area of minimal surfaces in AdS_3 ending on generic smooth boundary contours. The equations are derived from the continuum limit of the AMSV result for null polygonal boundary contours. Remarkably these continuum equations admit exact solutions in some special cases. In particular we describe a novel exact solution which interpolates between the circle and 4-cusp solutions.
A half-BPS circular Wilson loop in maximally supersymmetric SU(N) Yang-Mills theory in an arbitrary representation is described by a Gaussian matrix model with a particular insertion. The additional entanglement entropy of a spherical region in the presence of such a loop was recently computed by Lewkowycz and Maldacena using exact matrix model results. In this talk I will utilise the supergravity solutions that are dual to such Wilson loops in large representations to calculate this entropy holographically.
In this talk I will explain how to compute three-point functions of N=4 SYM theory in the planar limit for tree level and one-loop in perturbation theory. First I will recall how to formulate the problem of computing the three-point function of operators with determined R-charges in the language of integrable spin chains. In the su(2) sector, the tree-level three point function can be obtained in terms of determinants, whose large R-charge limit can be taken explicitly. Then I will report a systematic method to compute the su(2) three point function at higher loops.
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.