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.

Discussion of "A spacetime derivation of the Lorentzian OPE inversion formula” by Simmons-Duffin, Stanford and Witten. [1711.03816]

In this talk I will present recent results on the Bethe/Gauge correspondence obtained together with Mathew Bullimore and Hee-Cheol Kim. I will describe new ingredients of the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2,2) supersymmetric gauge theories. In particular, I will show how to construct off-shell Bethe states as orbifold defects in the A-twisted supersymmetric gauge theory and study their correlation functions. It will allow us to include aspects of algebraic Bethe ansatz in the correspondence. In particular, I will show how to interpret spin chain R-matrices as correlation functions of Janus interfaces for mass parameters.

Discuss 1710.09580

The Information Paradox represents a strong consistency challenge for any quantum theory of gravity. The study of black hole internal structure in String Theory offers the potential to resolve this paradox. I will give an overview of recent work on constructing families of smooth horizonless supergravity solutions describing black hole microstates. Where applicable, I will present a holographic description of these solutions. I will also discuss the physics of an observer falling into a black hole.

Supersymmetric localization is a powerful technique to evaluate a class of functional integrals in supersymmetric field theories. It reduces the functional integral over field space to ordinary integrals over the space of solutions of the off-shell BPS equations. The application of this technique to supergravity suffers from some problems, both conceptual and practical. I will discuss one of the main conceptual problems, namely how to construct the fermionic symmetry with which to localize. I will show how a deformation of the BRST technique allows us to do this. I will then sketch a computation of the one-loop determinant of the super-graviton that enters the localization formula for BPS black hole entropy.

Review of 1710.03934v1

We will discuss "From 3d duality to 2d duality" https://arxiv.org/abs/1710.00926 by Aharony, Razamat and Willett.

Any four dimensional N=2 superconformal field theory (SCFT) contains a subsector of local operator which is isomorphic to a two dimensional chiral algebra. If the 4d theory possesses N=3 or N= 4 superconformal symmetry, the corresponding chiral algebra is an extension the N=2 or (small) N=4 super-Virasoro algebra respectively. In this talk I will present some results on the classification of N=4 chiral algebras and discuss if they can correspond to a 4d theory.

I will discuss integrability in the context of planar AdS4/CFT3, where the CFT is the so-called ABJ model depending on two t'Hooft couplings. When the two couplings are equal, this reduces to the ABJM theory, whose integrable structure is well understood but depends on an unspecified interpolating function of the coupling. I will motivate a proposal that the most general ABJ case is also integrable, and that the two coupling constants l1 and l2 recombine into a single interpolating function h( l1 , l2 ) , so that the spectrum is a function of h only. Extending and idea by N. Gromov and G. Sizov on the ABJM case, an explicit conjecture for the form of h(l1, l2) wil be made, based on the comparison between integrability and localization results. The talk is based on the paper hep-th/1605.04888 with N. Gromov and F. Levkovich-Maslyuk.

I will start by sketching the computation of the topologically twisted index on H2xS1 and its evaluation in ABJM theory in the large N limit with k=1. Then after, I will review the key points behind the construction of magnetically charged (hyperbolic) AdS4 black holes on STU gauged SUGRA and will conclude by stating how the aformentioned index -- upon extremization -- coincides with the entropy of the latter black holes in the large N limit (with k=1).

The goal of this talk is twofold. Firstly, I would like to popularize the segmented string approach for solving the classical string dynamics on certain symmetric spacetimes where the string motion is integrable. This allows for an exact discretization which renders the equation of motion discrete in both space and time. The corresponding string solution is a segmented string. I will review the properties of segmented strings and relate them to discrete-time Toda-type lattices. The second goal of the talk is to understand a concrete setup: a (segmented) string hanging from the boundary of three-dimensional AdS spacetime. According to the gauge/gravity duality, the string in the bulk is dual to a flux tube between a quark-antiquark pair in the boundary field theory. We assume that the string is initially (quasi-)static. Perturbing one of the endpoints creates a large propagating wave on the string. The non-linear time-evolution produces a number of interesting phenomena: energy cascades, pair-creation of cusps, and evaporating regions on the string. If time permits, I will also talk about the string worldsheet as a simple model for gravity, chaos, out-of-time-order four-point functions, and segmented membranes.

Given some chiral conformal field theory (also known as a vertex operator algebra in the mathematics literature), a natural but highly non-trivial task is to classify its representation theory. In this talk, I will use some well known examples of conformal field theories, such as the Virasoro minimal models, to show how certain hard questions in representation theory can be neatly rephrased as comparatively easy questions in the theory of symmetric polynomials. After a brief overview of the theory of symmetric polynomials, I will show how they can be used to classify irreducible representations.