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.

Inspired by the multiplicative nature of the Ramanujan modular discriminant, Delta, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present some identities arising from q-expansions as well as relations to the sporadic Mathieu group M24.

Motivated by either condensed matter or quantum gravity holographic considerations, I will discuss some preliminary work on how to compute the time evolution in Renyi entropies in 2d CFTs in the large c limit for thermal states perturbed by localized primary operators. Time permitting, I will comment on the potential relation between this work and previous holographic calculations in the context of the EPR=ER conjecture.

Is there a consistent patching for double manifolds? I shall demonstrate that the solution of the strong section condition leads to exact 3-form field strengths. I shall also prove that the consistency of the examples presented so far depends on the choice of the atlas, and so they are not general covariant. Then I shall suggest a new construction which resolves some of the puzzles and possibly specifies the appropriate spaces up to homotopy.

We classify the possible linear unfolded equations for propagating bosonic higher-spin tensor fields in AdS_3 backgrounds. Doing this we reproduce the existing topologically massive and new topologically massive (higher)-spin systems whose content we clarify. We find systems that generalise various critical gravities to higher-spins.

We discuss entanglement and Renyi entropies in two-dimensional conformal field theories with extended symmetry algebras of W-type, in the semiclassical (large-c) limit. From the CFT perspective, the computation of these non-local observables involves the study of semiclassical conformal blocks in theories with additional conserved currents beyond the stress tensor. From an AdS perspective, the problem can be tackled using recent holographic proposals in terms of Wilson lines in the dual three-dimensional higher spin theories. We discuss non-trivial examples exhibiting the agreement between bulk and boundary computations.

I discuss the quantization of a perfect fluid. This differs from textbook QFT, because of the presence of vortex modes, which map to an infinite collection of quantum mechanical free particles rather than harmonic oscillators. As a result, there is no Fock space and no S-matrix. I argue that there exists, nevertheless, a consistent effective field theory description, valid at large distances and times.