Gravity theories naturally allow for edge states generated by non-trivial boundary-condition preserving diffeomorphisms. I present a specific set of boundary conditions inspired by near horizon physics, show that it leads to soft hair excitations of black hole solutions and discuss implications for black hole entropy.

2D rational conformal field theories (RCFTs) are typically thought of as being the “nicest” interesting CFTs we can study: They have large enough symmetry so that there are only a finite number of primary fields, but they also have applications to the real world (e.g., to various condensed matter systems). In this talk, I will describe a program that aims to understand connections between exotic 4D theories with N=2 superconformal symmetry and more down-to-earth 2D RCFTs, thereby enriching our understanding of both.

There are many reasons to consider perturbative QFT around curved backgrounds, but it is often difficult to perform explicit computations in these settings. Progress in the study of scattering amplitudes (around a trivial background) suggests alternative perspectives to space-time Lagrangians and Feynman rules which could enable progress in the study of scattering on curved backgrounds. I will discuss one such alternative, known as double copy, with a particular focus on gluon and graviton scattering around non-linear plane wave backgrounds

I will revisit the well-known construction of 5d SCFTs from M-theory on a CY3 singularity. Upon massive deformation, such 5d SCFTs are often expected to have 5d N=1 supersymmetric gauge theory descriptions at low energy. I will present a new way to study these 5d ``gauge theory phases'' systematically using type-IIA string theory, and I will comment on the phenomenon of "UV duality." Along the way, I will discuss some slightly subtle properties of the 5d N=1 Coulomb branch prepotential.

In two dimensional topological phases of matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, particle world lines can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link. While sounding rather exotic, we believe that such phases of matter not only exist, but have actually been observed in quantum Hall experiments, and could provide a uniquely practical route to building a quantum computer. Possibilities have also been proposed for creating similar physics in systems ranging from superfluid helium to strontium ruthenate to semiconductor-superconductor junctions to quantum wires to spin systems to graphene to cold atoms.

The geometry of the moduli space of 4d \mathcal{N}=2 moduli spaces, and in particular of their Coulomb branches (CBs), is very constrained. In this talk I will show that through its careful study, we can learn general and somewhat surprising lessons about the properties of \mathcal{N}=2 super conformal field theories (SCFTs). Specifically I will show that we can prove that the scaling dimension of CB coordinates, and thus of the corresponding operator at the SCFT fixed point, has to be rational and it has a rank-dependent maximum value and that in general the moduli spaces of \mathcal{N}=2 SCFTs can have metric singularities as well as complex structure singularities. Finally I will outline how we can explicitly perform a classification of geometries of \mathcal{N}\geq3 SCFTs and carry out the program up to rank-2. The results are surprising and exciting in many ways.

The AdS/CFT duality maps supersymmetric heavy operators with conformal dimension of the order of the central charge to asymptotically AdS supergravity solutions. I'll show how, by studying the quadratic fluctuations around such backgrounds, it is possible to derive 4-point correlators of two light and two heavy states in the supergravity approximation. Then by using this input, I'll discuss how to reconstruct standard supergravity correlators between four (single particle) operators. I'll present some explicit examples in the AdS3 setup relevant for the duality with the D1-D5 CFT.

I will adapt the Goldstone theorem to spontaneously broken boosts, and show that, while still predicting gapless Goldstone states, it is quite forgiving regarding the nature of such states. In particular, I will show that while for solids and superfluids the role of the boost Goldstone states is played by phonon single-particle states, for a Fermi liquid such a role is played by the particle-hole continuum, that is, by two-particle states.

Fixed points are crucial in understanding the RG flow of quantum field theories. The conformal bootstrap has proved a wonderful tool in determining the properties of CFTs at fixed points but tends to require guidance in terms of what symmetries to impose and what is the spectrum of relevant operators. Here I review what can be said in general by using the time honoured epsilon expansion. Although qualitatively this is not nowadays the most efficient method it provides qualitative information about possible fixed points. Finding fixed points which cannot be linked to the epsilon expansion could provide a clue to non Lagrangian theories.

Extensions of target space T-duality to non-Abelian isometry groups and even to spaces without isometry have found recent utility within the AdS/CFT correspondence and have played a central role in the development of new classes of integrable string backgrounds called $\eta$ and $\lambda$-models. After a pedagogical introduction to the topic I will outline some recent results concerning the open sector of $\lambda$-models and the interpretation of these theories within the formalism of double field theory.

We propose non-linear formally consistent equations of motion for the Type-B Higher Spin Gravity that is dual to the free fermion or to the Gross-Neveu model, depending on the boundary conditions. The equations are directly obtained from the first principles: the gauge invariance of the CFT partition function on an arbitrary background. We show that the system has a vacuum solution describing general higher-spin flat backgrounds and demonstrate that the respective linearized system describes propagation of higher-spin fields over such backgrounds, reproducing all the structures that are known to determine nonlinear higher-spin equations.

n this talk I will review the results of recent work in collaboration with Cecilia De Fazio, Benjamin Doyon and István M. Szécsényi. We studied the entanglement of excited states consisting of a finite number of particle excitations. More precisely, we studied the difference between the entanglement entropy of such states and that of the ground state in a simple bi-partition of a quantum system, where both the size of the system and of the bi-partition are infinite, but their ratio is finite. We originally studied this problem in massive 1+1 dimensional QFTs where analytic computations were possible. We have found the results to apply more widely, including to higher dimensional free theories. In all cases we find that the increment of entanglement is a simple function of the ratio between region's and system's size only. Such function, turns out to be exactly the entanglement of a qubit state where the coefficients of the state are simply associated with the probabilities of particles being localised in one or the other part of the bi-partition. In this talk I will describe the results in some detail and discuss their domain of applicability. I will also highlight the main QFT techniques that we have used in order to obtain them analytically and present some numerical data.

Abstract: We define indices for topologically twisted supersymmetric theories from two to five dimensions. We apply them to the holographic study of AdS black holes, black strings and domain-walls across dimensions.

There are two approaches to duality covariant first order alpha-prime corrections to the heterotic string. One is based on an extension of the duality structure, and the other relies on deformed gauge transformations. I will introduce an all order framework from which both approaches can be derived, proving their equivalence and extending them to higher orders.

Chern-Simons theories coupled to fundamental matter have a wide variety of applications ranging from Quantum Hall effect to Quantum gravity via AdS/CFT. These theories enjoy a strong weak duality that has been tested to a very good accuracy via large N computations, such as thermal partition functions, and S matrices. Supersymmetric Chern-Simons theories are equally interesting since they have a self duality and relate to non-supersymmetric theories via RG flows. In the N=2,3 supersymmetric Chern-Simons matter theories, the four point amplitude computed to all orders in the 't Hooft coupling is not renormalised! It is a unique situation in a quantum field theory that the scattering amplitude doesn't receive loop corrections. This indicates the presence of powerful symmetry structures within the theory. This also suggests that higher point amplitudes may be easier to compute using four point amplitudes as building blocks. These higher point amplitudes not only serve as a testing tool for duality but also a probe into the symmetry structure of the theory. As a first step towards this goal, we begin by computing arbitrary n point tree level amplitudes in the N=2 theory via BCFW recursion relations. We then show that the four point tree level amplitude enjoys a dual superconformal symmetry. Since the all loop four point amplitude is tree level exact, it follows that the dual superconformal symmetry is exact to all loops. This is in contrast to highly supersymmetric examples such as N=4 SYM and N=6 ABJM, where the dual superconformal symmetry is in general anomalous. Furthermore, we show that the superconformal and dual superconformal symmetries generate an infinite dimensional Yangian symmetry for the four point amplitude. If these symmetries persist to higher point amplitudes, this suggests that the N=2 superconformal Chern-Simons matter theory may be integrable.

I will describe a new procedure for coarse-graining over the gravitational degrees of freedom inside a surface in the context of AdS/CFT. I will prove that in general dimensions, this coarse-graining gives an explanation of an infinite family of gravitational area laws. In three bulk dimensions, it is also straightforward to derive the precise dual of these area laws as strong subadditivity of the von Neuman entropy in the dual CFT. I will discuss a number of implications of this, which include an explanation for the geometric bulk phenomenon of extremal surface barriers

Kostas Skenderis: Title: "Towards a general AdS/Ricci-flat correspondence" Abstract: The AdS/Ricci-flat (AdS/RF) correspondence is a map between families of asymptotically locally AdS solutions on a torus and families of asymptotically flat spacetimes on a sphere. In this talk I will discuss how to relax these restrictions for linearized perturbations around solutions connected via the original AdS/RF correspondence. This correspondence should allow us to develop a detailed holographic dictionary for asymptotically flat spacetimes. Andrei Starinets: TBA

We discuss the computation of all-point correlation functions in the SYK model, at leading order in 1/N. The result has remarkable simplicity and structure. The result is general, holding for any theory in which one forms higher-point correlators by gluing together four-point functions; for instance, large N vector models and tensor models. It implies specific singularity structure of analytically extended OPE coefficients. In particular, the analytically extended OPE coefficients of the single-trace operators encode the OPE coefficients of the double-trace operators

The spatially modulated self-organization of strongly-correlated electrons is central in describing the phenomenology of many condensed matter systems, such as the cuprates and the manganites. Holography can describe spontaneous formation of various kinds of density waves in a strongly-coupled media and provides toy-model effective field theories able to capture important phenomenological features, such as the low-temperature scaling of the conductivity. Appropriate UV completions of the holographic EFT can also describe the spontaneous generation of the spatial features themselves.