I will give an overview of the topic and I will discuss the non-perturbative derivation of 3-point functions of scalar operators, symmetry current and energy momentum tensor in momentum space, including renormalization and anomalies. Based on 1805.12100, 1711.09105, 1510.08442, 1304.7760.

We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge Q, obeying Q2=H, where H is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the QV deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2×S2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.

I will describe some counterexamples to (weak) cosmic censorship in anti-de Sitter spacetime that have been found recently. These are solutions in which the curvature grows without bound in a region of spacetime visible to infinity. I will also discuss a surprising connection between some of these counterexamples and an apparently unrelated conjecture called the weak gravity conjecture.

TBA

I will summarise old and recent developments on the classification and solution of Rational Conformal Field Theories in 2 dimensions using the method of Modular Differential Equations. Novel and exotic theories are found with small numbers of characters and simple fusion rules, one of these being the Baby Monster CFT. Correlation functions for many of these theories can be computed using crossing-symmetric differential equations.

TBA

I and my collaborator, T.Nosaka, revisited minimal N = 4 Chern-Simons theories from its exact S3 partition function, which reduces to finite-dimensional matrix models by supersymmetric localization. We found some new aspects of this interesting model and main results are listed below. [1] The integration in a matrix model of S3 partition function may be performed completely by using the technique called the Fermi-gas analysis. [2] The resulting partition function completely factorized into that of pure CS theory for two gauge groups and an analogous contribution for the bifundamental hypermultiplet. We call this complete factorization. [3] We presented the all order ’t Hooft expansion of the free energy and discussed the connection to the higher-spin theory in the dual gravity side. [4] The level/rank (or Seiberg-like) duality, which is expected from the Hanany-Witten transition in the type IIB brane realization, was confirmed from the factorized partition function up to an overall factor, which may be a signal of existence of some decoupled sector. If time permits, I may touch our ongoing analysis of such decoupled sector more precisely by using a superconformal index.

I discuss some aspects of boundary conformal field theories (bCFTs) with an emphasis on space-time dimensions greater than two. I will demonstrate that free bCFTs have a universal way of satisfying crossing symmetry constraints. I will introduce a simple class of interacting bCFTs where the interaction is restricted to the boundary. Finally, I will discuss relationships between boundary trace anomalies and boundary limits of stress-tensor correlation functions. (Tea and biscuits + wine at the end!)

We review the global formulation of higher spin gravity using topological field theory methods and non-commutative geometry and related recent progress in constructing micro states for black holes, domain walls and cosmologies.

TBA

The talk will be a review of some of the properties of defects that can be supported by at least some integrable field theories describing massive scalar particles, including the apparently central role played by energy and momentum stored by the defect. The sine-Gordon model is the simplest of these, and for this talk the main example, but there are many others. There are a number of open problems in both the classical and quantum field theory that will be described.

The SYK model, and more generally, tensor models, are a new class of large N quantum field theories. 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.

I will discuss the properties of a family of four-dimensional CFTs, recently proposed by O.Gurdogan and myself, emerging as a double scaling limit of weakly coupled and strongly gamma-twisted N=4 SYM theory. These non-unitary CFTs inherit the integrability of N=4 SYM in the planar limit and present a unique opportunity of a non-perturbative study of four-dimensional conformal physics. Important physical quantities are dominated by a limited subset of Feynman graphs (such as "fishnet" graphs for the simplest, bi-scalar model). I present the results of exact calculation of some of these quantities, such as anomalous dimensions of local operators, some 3- and 4point correlation functions and scattering amplitudes, by means of spin chain techniques or the quantum spectral curve (QSC) approach originally proposed for N=4 SYM.

Anti-de-Sitter solutions play an important role in the gauge-theory/gravity correspondence, and understanding their properties has provided important insights into the dual field theories. We consider ADS solutions which are highly supersymmetric, in the sense that they preserve more than 16 supersymmetries, and show how how modified versions of the homogeneity theorems of Figureoa-O'Farrill, combined with aspects of the global properties of the geometries, can be used to classify these solutions.

In the talk I'll consider theories of weakly interacting higher spin particles in flat spacetime. We will focus on the four-point scattering amplitude at high energies and imaginary scattering angles. Both, the leading asymptotic of the amplitude and the first sub-leading correction in this regime turn out to be universal. The leading asymptotic is equal to the corresponding limit of the Veneziano amplitude. We will compute the first sub-leading correction using a model of relativistic strings with massive endpoints and argue that it is unique using holography, the effective theory of long strings and bootstrap techniques.

We discuss the applicability of the Quantum Spectral Curve approach (the most advanced and precise method initially developed for the spectrum of anomalous dimensions of planar N=4 SYM) to the problem of computing structure constants. We give a pedagogical introduction to the QSC formalism for the anomalous dimensions and then present our new results about a more general class observables.

We will discuss generalized circular Wilson loops and 1d CFT defined by correlators of operators inserted along the loop following arXiv:1706.00756 and some more recent work.

TRIANGULAR SEMINAR: We propose an integrability setup for the computation of correlation functions of gauge-invariant operators at any value of the 't Hooft coupling and at any order in the large Nc 't Hooft expansion in N = 4 SYM theory. In this multi-step proposal, one polygonizes the string worldsheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a non-planar four-point correlator of large half-BPS operators at one and two loops.

TRIANGULAR SEMINAR: New techniques of large N and large D allow to study analytically planar matrix quantum mechanics at strong coupling in a reliable way. Using these techniques, we found a remarkable phase transition in these systems, which is very naturally interpreted as a quantum version of the phenomenon of black hole formation in a gravitational collapse.
Based on 1701.01171, 1707.03431, 1709.07366, 1710.07263 and work in progress.

Non-abelian gauge theories underlie particle physics, including collision processes at particle accelerators. Recently, quantum scattering probabilities in gauge theories have been shown to be closely related to their counterparts in gravity theories, by the so-called double copy. This suggests a deep relationship between two very different areas of physics, and may lead to new insights into quantum gravity, as well as novel computational methods. This talk will review the double copy for amplitudes, before discussing how it may be extended to describe exact classical solutions such as black holes. Finally, I will discuss hints that the double copy may extend beyond perturbation theory.