This series consists of talks in the area of Superstring Theory.
I will talk about 4d N=2 gauge theories with a co-dimension-two full surface operator, which exhibit a fascinating interplay of supersymmetric gauge theories, equivariant Gromov-Witten theory and geometric representation theory. For pure Yang-Mills and N=2* theory, a full surface operator can be described as the 4d gauge theory coupled to a 2d N=(2,2) gauge theory. By supersymmetric localizations, we present the exact partition functions of both 4d and 2d theories which satisfy integrable equations.
We exactly evaluate the partition function (index) of N=4 supersymmetric quiver quantum mechanics in the Higgs phase by using the localization techniques. We show that the path integral is localized at the fixed points, which are obtained by solving the BRST equations, and D-term and F-term conditions. We turn on background gauge fields of R-symmetries for the chiral multiplets corresponding to the arrows between quiver nodes, but the partition function does not depend on these R-charges. We give explicit examples of the quiver theory including a non-coprime dimension vector.
I will discuss various aspects of non-relativistic field theories on a curved, background spacetime. First things first, we need to know what sort of geometry these theories couple to, as well as the symmetries we ought to impose. I will argue that Galilean-invariant theories should be coupled to a form of Newton-Cartan geometry in which one enforces a one-form shift symmetry, which amounts to a covariant version of invariance under Galilean boosts.
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 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.