The cross or soft anomalous dimension matrix describes the renormalization of Wilson loops with a self-intersection and is an important object in the study of infrared divergences of scattering amplitudes. I will discuss it for the case of the Maldacena--Wilson loop in N=4 supersymmetric Yang--Mills theory, considering both the strong-coupling description in terms of minimal surfaces in AdS5 as well as the weak-coupling side up to the two-loop level. In either case, the coefficients of the cross anomalous dimension matrix can be expressed in terms of the cusp anomalous dimension. The strong-coupling description displays a Gross--Ooguri phase transition and I will argue that the cross anomalous dimension is an interesting object to study in an integrability-based approach.

M-theory is currently our best candidate for a theory of everything, but remains mysterious. We know M-theory has M2- and M5-branes. The low-energy theory on a stack of coincident M2-branes is well-understood: it is maximally supersymmetric Chern-Simons-matter theory. However, the low-energy theory on a stack of coincident M5-branes remains poorly-understood: it is a maximally supersymmetric theory of self-dual strings with zero tension. In this talk I will discuss one type of probe of the M5-brane theory, namely self-dual strings with infinite tension. These play a role analogous to Wilson lines in gauge theories, but are two-dimensional surfaces rather than lines, and hence are called Wilson surfaces. I will describe holographic calculations of entanglement entropy associated with these infinite-tension self-dual strings, from which we extract a key parameter characterizing them, their central charge. This provides a count of the number of massless degrees of freedom living on them, and thus may shed light on some of the fundamental degrees of freedom of M-theory.

In my talk I will give a review on the logarithmic terms that appear in the entanglement entropy, their relation to conformal anomaly and the geometry of the entangling surfaces. I will discuss how the presence of boundaries may effect these terms.

We study the nearly AdS(2) geometry of nearly extremal black holes in N = 2 supergravity in four dimensions. In the strictly extreme limit the attractor mechanism for asymptotically flat black holes states that the horizon geometries of these black holes are independent of scalar moduli. We determine the dependence of the near extreme geometry on asymptotic moduli and express the result in simple formulae that generalize the extremal attractor mechanism to nearly extreme black holes. This is a nAttractor mechanism. We discuss the dependence of the near horizon theory on the scales introduced by generic attractor flows.

After briefly reviewing dark energy, dS vacua and the standard model of cosmology, I will discuss recent conjectures that say that metastable dS vacua cannot arise in string theory. These conjectures lead to interesting observational predictions and are currently being tested experimentally. On the theoretical side I will discuss the support for these conjectures as well as the status of explicit counter examples like the KKLT and LVS scenario.

Black holes appear to lead to information loss, thus violating one of the fundamental tenets of Quantum Mechanics. Recent Information-Theory-based arguments imply that information loss can only be avoided if at the scale of the black hole horizon there exists a structure (commonly called fuzzball or firewall) that allows information to escape. I will discuss the highly-unusual properties that this structure must have and how these properties emerge in the realization of this structure in String Theory via branes, fluxes and topology. I will then describe the implication of this structure for AdS_2 holography.

After-talk reception at Staff Common Room King's Building

I will discuss consistent reductions of pure AdS gravity in 3D and 5D to 2D and use them to derive effective actions for the near conformal quantum mechanics dual to the near extremal BTZ and Kerr-AdS5 black holes, respectively. The role of AdS2 gauge fields and their boundary conditions will be discussed in detail.

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.