Quantum Fields and Strings

Instantons and W-bosons in 5d N=2 Yang-Mills theory arise from a circle compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding self-dual strings, respectively. We study an index which counts BPS instantons with electric charges in Coulomb and symmetric phases. We first prove the existence of unique threshold bound state of U(1) instantons for any instanton number. By studying SU(N) self-dual strings in the Coulomb phase, we find novel momentum-carrying degrees on the worldsheet. The total number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory. We finally propose that our index can be used to study the symmetric phase of this theory, and provide an interpretation as the superconformal index of the sigma model on instanton moduli space.

Quantum corrections to three-point functions of scalar single trace operators in planar ${\cal N}=4$ Super-Yang-Mills theory are studied using integrability. At one loop, we find  new algebraic structures that not only govern all two loop corrections to the mixing of the operators but also automatically incorporate all one loop diagrams correcting the tree level Wick contractions. Speculations about possible extensions of our construction to all loop orders are given. We also match our results with the strong coupling predictions in the classical (Frolov-Tseytlin) limit. 

I will explain some recent exact developments in N=2 SUSY gauge theories on 3-sphere and its deformations. I will begin by the analysis of Killing spinors and their generalization which are necessary to construct SUSY theories on curved spaces. Then I will sketch the exact computation of partition function using SUSY localization and present a general formula. Some applications to the physics of M5-branes will also be discussed.

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is still an open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.

In this talk we discuss a proposed dual matrix formulation of N = 4 Super Yang-Mills on R^4 coupled to 4D Einstein supergravity. We review the evidence accumulated so far in favor of this proposal, which includes a successful match of the symmetries of the continuum theory, and the computation of MHV gluon and graviton scattering amplitudes in terms of matrix model correlators. We also discuss some avenues of ongoing investigation.

Three-dimensional fluids with nontrivial vorticity can be described holographically. It is well-known that the Kerr-AdS geometry gives rise to a 'cyclonic' flow. Lorentzian Taub--NUT--AdS_4 geometries give rise to a rotating fluid with vortex flow.

The boundary conditions of general black holes in asymptotically flat spacetimes can be modified such that a conformal symmetry emerges. The black holes with asymptotic geometry modified in this manner satisfy the equations of motion of minimal supergravity in one dimension more. Their symmetry suggests that a dual conformal field theory description exists that can account for the black hole entropy even in the case of black holes that are far from extremality.

We evaluate the partition function of three dimensional general relativity with a negative cosmological constant, including all known perturbative and non-perturbative contributions to the sum over geometries.

I will present a newly found duality between an infinite class of 3-dimensional N=4 gauge theories at their conformal IR fixed point and type IIB string theory solutions. This correspondence gives a new tool to explore the strongly coupled phase of the supersymmetric gauge theories in question.

We study the constraints imposed by the existence of a single higher spin conserved current on a three dimensional conformal field theory. A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of $N$ free bosons or free fermions. This is an extension of the Coleman-Mandula theorem to CFT's, which do not have a conventional S matrix. We also briefly discuss the case where the higher spin symmetries are ``slightly'' broken.