We numerically construct asymptotically anti-de Sitter (AdS) black holes in four dimensions that contain only a single Killing vector field. These solutions, which we coin black resonators, link the superradiant instability of Kerr-AdS to the nonlinear weakly turbulent instability of AdS by connecting the onset of the superradiance instability to smooth, horizonless geometries called geons. Furthermore, they demonstrate non-uniqueness of Kerr-AdS by sharing asymptotic charges. Where black resonators coexist with Kerr-AdS, we find that the black resonators have higher entropy. Nevertheless, we show that black resonators are unstable and comment on the implications for the endpoint of the superradiant instability.

Ambitwistor strings are holomorphic string theories whose target space is the space of complex null geoedesics in complexified space-times. I will explain how these theories explain the origin of the scattering equations in twistor strings and the CHY formulae in arbitrary dimensions and provide a reformulation of standard gauge, gravity and other theories in a holomorphic infinite tension analogue of conventional string theories. I will show how these results extend to 1-loop both on a torus and on a nodal Riemann sphere, and perhaps to higher loops.

In this talk I will consider brane configurations that include NS5 branes, orientifold planes and anti-branes. I will argue that the class of field theories that live on such brane configurations admit Seiberg duality. Interactions between branes and orientifold planes will be given a field theory interpretation. In particular a certain repulsive interaction will lead to a non-trivial Coleman-Weinberg potential and dynamical symmetry breaking. I will also discuss the case of type 0' strings and chiral symmetry breaking of the form SU(Nf)xSU(Nf)-->SU(Nf) in a QCD-like theory.

There exist, in d=2+1 dimensions, field theories that are supersymmetric but non-relativistic. I will show that the low-energy physics of these theories is that of the fractional quantum Hall effect. Supersymmetry provides enough analytic control to explicitly derive the ground state wavefunctions and their excitations.

We study the free energy of the three dimensional N=2 supersymmetric Chern-Simons-Matter theory dual to AdS4 times toric seven dimensional Sasaki-Einstein manifold. Although it is not known in general how to construct the CSM theory from the geometric data of the 7d SE manifold (which is called toric diagram), the free energy in the large N limit may be derived. We present the free energy as a quartic polynomial of trial R-charges for generic toric diagram with up to 6 vertices, and some particular diagrams with 8 vertices. The free energy reproduces the Martelli-Sparks-Yau volume function.

We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2 x S^2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.

Program at: http://www.mth.kcl.ac.uk/~k1469797/ECRSEMPS15/

We consider bound states of strings which arise in 6d (1,0) SCFTs that are realized in F-theory in terms of linear chains of spheres with negative self-intersections 1,2, and 4. These include the strings associated to N small E8 instantons, as well as the ones associated to M5 branes probing A and D type singularities in M-theory or D5 branes probing ADE singularities in Type IIB string theory. We find that these bound states of strings admit (0,4) supersymmetric quiver descriptions and show how one can compute their elliptic genera.

We will discuss the construction of type IIA mirror a la Strominger Yau Zaslow prescription and its M-theory uplift in the delocalized limit {resulting in black M3-branes=asymptotically black M5-branes wrapping large integer sum of two-spheres in AdS_5xM_6} of type IIB backgrounds involving non-Kaehler resolved warped deformed conifolds in the presence of [fractional]D3 and wrapped D7-branes relevant to thermal QCD with fundamental quarks. We will show that the local T^3 relevant to SYZ mirror construction obeys the same constraint as the maximal T^2-invariant special Lagrangian three-cycle of deformed conifolds. We also discuss evaluation of the SU(3) structure torsion classes of the type IIB background and show its (approximate) Kaehlerity. We will also discuss thermodynamical/hydrodynamical properties as well as evaluation of a variety of transport coefficients {from correlation functions of gauge and metric fluctuations}, speed of sound and QCD deconfinement temperature consistent with lattice data.

Hydrodynamic integrable systems are characterized by an infinite number of conserved quantities and can be described in terms of integrable partial differential equations. I will focus on the periodic Intermediate Long Wave (ILW) system, both at the classical and quantum level. The quantum system has not been solved yet, if not in a particular limit (the Benjamin-Ono limit) which is related to the AGT correspondence. In this talk I will show how a particular two dimensional N=(2,2) gauge theory on S^2 can be used to determine the spectrum of the quantum ILW system via Bethe Ansatz equations, as well as the norm of the eigenstates. In addition the partition function of this theory computes genus zero Gromov-Witten invariants for the ADHM instanton moduli space, thus relating quantum cohomology to quantum hydrodynamics.

I will discuss recent progress in formulating superconformal quantum mechanics models which describe the (2,0) theory and N=4 super Yang-Mills in discrete light-cone quantisation.

I will give a pedagogical introduction to recent developments in the study of N=4 super-Yang-Mills scattering amplitudes, and super-Wilson loops with a focus on their symmetries.

It has been conjectured that the fundamental theory of strings and branes has an $E_{11}$ symmetry. I will explain how this conjecture leads to a generalized space-time, which is automatically equipped with its own geometry, as well as equations of motion for the fields that live on this generalized space-time.

In the past few years we have seen that the bootstrap approach to higher-dimensional conformal field theories (CFTs) can be surprisingly powerful. In particular, we are finally able to put the crossing symmetry equations to good use and extract nontrivial information about the spectrum and three-point functions in a generic CFT. In this talk I will discuss the application of these ideas to superconformal field theories, focussing on N=2 and N=4 theories in four dimensions. In those theories there exists a subsector where the crossing symmetry equations can be solved analytically. Together with the numerical analysis of the remaining constraints we can learn a great deal about the nonperturbative structure of these superconformal field theories.

The study of high energy amplitudes in string theory provides an interesting arena to study several issues in quantum theories of gravity. I will focus on a conceptually very simple situation where a perturbative graviton scatters against a stack of D-branes and I will discuss phenomena, such as the emergence of tidal forces, the restoration of unitarity through resummation of diagrams and how the Regge behaviour of string theory is crucial to avoid causality violations

I will discuss recent progress in formulating superconformal quantum mechanics models which describe the (2,0) theory and N=4 super Yang-Mills in discrete light-cone quantisation.

It is often said that soliton contributions to perturbative processes in QFT are exponentially suppressed by a form-factor. We will provide a derivation of this form-factor by studying the soliton-antisoliton pair-production amplitude. This reduces to the calculation of a matrix element in the quantum mechanics on the soliton moduli space. We will investigate the conditions under which the latter leads to suppression. Extending this framework to instanton-solitons in five-dimensional Yang-Mills theory leaves open the possibility that such contributions will not be suppressed.

I will review recent work on the formulation of self-dual higher (categorified) gauge theory in six dimensions using twistor theory.

I will review how integrability can be used to understand the spectral problem (including massless modes) of Type IIB string theory on AdS3 x S3 x T4 with R-R flux. I will then show how integrability emerges in the dual CFT2. This provides arguably the first non-BPS test of the planar AdS3/CFT2 correspondence in the literature and gives strong evidence in identifying particular points in the moduli space of the dual theories.

I will discuss conformal bootstrap for SCFTs with four supercharges (eight superconformal charges) between two and four dimensions in a unified language. The special cases of interest are (2,2) SCFTs in d=2, N=2 SCFTs in d=3, and N=1 SCFTs in d=4. I will show how a large class of superconformal blocks can be found from the Casimir differential equation. I will describe the numerical bounds arising from the two independent bootstrap equations of the four-point function involving a chiral field and its conjugate. The bound involves three kinks, one of which corresponds to the IR fixed point of the Wess-Zumino model, and the other two remain mysterious.