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.

We discuss the presence of phonons and the interplay between spontaneous and explicit breaking of translations in the context of holography. Using two different bottom-up models we show the existence of transverse and longitudinal phonons, whose properties are in perfect agreement with elastic theory and hydrodynamics. We focus our attention on the elastic and transport features of the dual QFT also in the presence of a small explicit breaking. We conclude speculating about the possibility of having gravitational duals for strongly coupled viscoelastic materials.

I will present a new approach to study the RG flow in 3d N=4 gauge theories, based on an analysis of the Coulomb branch of vacua. The Coulomb branch is described as a complex algebraic variety and important information about the strongly coupled fixed points of the theory can be extracted from the study of its singularities. I will use this framework to study the fixed points of USp(2N) gauge theories with fundamental matter, revealing some surprising features at low amount of matter.

Superconformal field theories placed in nontrivial background fields for the metric and the continuous global symmetries exhibit a rich web of RG flows across dimensions. I will discuss several examples of such flows and emphasize some of their universal features. In addition, I will employ non-perturbative tools such as 't Hooft anomaly matching, a-, F-, and c-extremization, and holography to gain a quantitative understanding of some aspects of these theories. Finally, I will discuss the relevance of these results for a microscopic understanding of the entropy of supersymmetric black holes and strings in AdS.

From a modern viewpoint the "S-matrix bootstrap" is the idea that general consistency conditions can be used to obtain quantitative constraints on scattering amplitudes. I will discuss the assumptions behind this approach, open questions about the structure of amplitudes, and discuss some fundamental results from the sixties and seventies. In the second part of the talk I will treat two modern approaches which were inspired by recent results on the conformal bootstrap, and show how they can be used to constrain scattering amplitudes in non-trivial ways.

We describe the leading and sub-leading multi-soft behavior of tree level gluon amplitudes and an underlying two-dimensional description of such scenarios where the soft limits are currents related to asymptotic symmetries of YM theory. Such kinematic limits allow us to explore the algebra of these two dimensional currents and we comment on their CFT interpretation. Then we explore a possible two-dimensional description of certain amplitudes in massive scalar QFT’s.

I will discuss the computation of the graviton one-loop determinant in the BTZ black hole background with certain chiral boundary conditions at the AdS boundary. These boundary conditions were proposed by Compere, Song and Strominger and were shown to modify the asymptotic symmetry algebra from a sum of left and right Virasoro algebras to a single right-moving Virasoro U(1) Kac-Moody. This implies that the holographic dual description possesses such global symmetry and so should be described by a warped conformal field theory (WCFT) instead of a standard CFT. In the talk I will overview the new boundary conditions and the concept of a WCFT, outline the computational method of obtaining the one-loop determinant from the "quasinormal" mode spectrum (highlighting elements which are unique to the new boundary conditions) and discuss the implications of the results for the boundary field theory.

I will start with briefly describing the HISH ( Holography In- spired Hadronic String) model and reviewing the fits of the spectra of mesons, baryons, glueballs and exotic hadrons. I will present the determination of the hadron strong decay widths. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as Γ = πATL/2 where T and L are the tension and length of the string and A is a dimensionless universal constant. The partial width of a given decay mode is given by Γ_i/Γ = Φ_i exp(−2πCm^2_sep/T) where Φi is a phase space factor, msep is the mass of the ”quark” and ”antiquark” created at the splitting point, and C is a dimensionless coefficient close to unity. I will show the fits of the theoretical results to experimental data for mesons and baryons. I will examine both the linearity in L and the expo- nential suppression factor. The linearity was found to agree with the data well for mesons but less for baryons. The extracted coefficient for mesons A = 0.095 ± 0.015 is indeed quite universal. The exponential suppression was applied to both strong and radiative decays. I will discuss the relation with string fragmentation and jet formation. I will extract the quark-diquark structure of baryons from their decays. A stringy mechanism for Zweig sup- pressed decays of quarkonia will be proposed and will be shown to reproduce the decay width of Υ states. The dependence of the width on spin and flavor symmetry will be discussed. We further apply this model to the decays of glueballs and exotic hadrons.