A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling Ï„ and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real Ï„ axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories.

I will talk about the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background. The gravitational functional integral localizes onto the cohomology of a global supercharge Q_eq, obeying (Q_eq)²=H, where H is a global symmetry of the background. This construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. I will 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 Qeq deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS₂×S² saddle.

I will first review the Batalin-Vilkovisky formalism and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. I will then move on and discuss recent developments in formulating higher gauge theory with Lie quasi-groupoids as gauge structure. Finally, I will explain how all these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of quasi-isomorphisms.

This will be presenting mainly some of my recent work, and also aspects of recent work of Herbert Spohn, both developed in parallel. The classical Toda system is a one-dimensional integrable many-body system, which can be seen either as a gas of particles or as a chain of degrees of freedom. Herbert has shown how the generalised Gibbs ensembles of the Toda chain can be obtained from a certain limit of the beta-ensemble in random matrix theory. Analysing and connecting the gas and chain viewpoints, I have obtained both the generalised Gibbs ensembles and generalised hydrodynamics from a quasiparticle scattering description. Thus we make a connection between quasiparticle scattering and random matrix theory.

In the first part of my talk I will give a brief introduction to the main features of the Entaglement Entropy of a bipartite system in Integrable Quantum Field Theories and Conformal Field Theories. Secondly I will discuss the results my collaborators and I obtained in our two papers. In particular, I will consider the Entaglement Entropy of a single connected region of a finite bipartite system in excited states described by one-dimensional massive free theories with finite numbers of particles. I will show that in the limit of large volume and large length of the region the excess of entanglement due to the presence of the particles with respect to the ground state takes a simple form and admits a "q-bit interpretation".

This talk will explore topological invariants of susy gauge theories, with some emphasis on index-like quantities and the notion of holonomy saddles. We start with 1d refined Witten index computations where the twisted partition functions typically show rational, rather than integral, behavior. We will explain how this oddity is a blessing in disguise and propose a universal tool for extracting the truely enumerative Witten indices. In part, this finally put to the rest a two-decade-old bound state problems which had originated from the M-theory hypothesis. Along the way, we resolve an old and critical conflict between Kac+Smilga and Staudacher/Pestun, circa 1999~2002, whereby the notion of holonomy saddles emerges and plays a crucial role. More importantly, the holonomy saddle prove to be universal features of supersymmetric gauge theories when the spacetime include a small circle. We explore them further for d=4, N=1 theories, with much ramifications on recent claims on Cardy exponents of their partition functions.

In recent years, more and more compactifications have emerged whose existence depends crucially on the presence of internal sources to the supergravity fields, such as D-branes and orientifold planes. I will review some solutions of this type in various dimensions, and illustrate their applications to holography and potentially to the problem of finding de Sitter solutions.

A solvable irrelevant deformation of AdS3/CFT2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed by Kutasov et al. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable T\bar{T}-deformations of two-dimensional CFTs. Thought of as a worldsheet sigma-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 in the IR and a linear dilaton vacuum of little string theory in the UV. In this talk, after giving an introduction to this class of solvable theories, I will present explicit results for their observables.

The cosmic censorship conjecture raises the question of whether classical gravitational dynamics can drive a low-energy configuration into an accessible regime of quantum gravity, with Planck-scale curvatures and energy densities visible by distant observers. I will present evidence that cosmic censorhip is violated in the quintessential phenomenon of General Relativity: the collision and merger of two black holes. It only requires a sufficient total angular momentum in a collision in high enough number of dimensions. Nevertheless, I will argue that even if cosmic censorship is violated in this and in some other know instances, its spirit remains unchallenged: classical relativity describes the physics seen by observers outside the black holes accurately, with only minimal quantum input that does not entail macroscopic disruptions.

We consider the energy of a (2+1)-d relativistic QFT on a deformation of flat space in either the quantum or thermal vacuum state. Looking at both free scalars and fermions, with and without mass (and in the scalar case including a curvature coupling) we surprisingly find that any deformation of flat space is always energetically preferred to flat space itself. This is a UV finite effect, insensitive to any cut- off. We see the same behaviour for any (2+1)-holographic CFT which we compute via the gravity dual. We consider the physical application of this to membranes carrying relativistic degrees of freedom, the vacuum energy of which then induce a tendency for the membrane to crumple. An interesting case is monolayer graphene, which experimentally is observed to ripple, and on large scales can be understood as a membrane carrying free massless Dirac degrees of freedom.

I will describe the one-dimensional complex conformal manifold that controls the infrared dynamics of a three-dimensional N=2 supersymmetric theory of three chiral superfields with a cubic superpotential. Two special points on this conformal manifold are the XYZ model and three decoupled copies of the critical Wess-Zumino model. The conformal manifold enjoys a discrete duality group and can be thought of as an orbifold of CP^1. I will discuss how to compute the spectrum of low lying operators and their OPE coefficients as a function of the coordinate on the conformal manifold using the epsilon-expansion and the numerical conformal bootstrap.

“We revisit Donaldson-Witten theory, that is the N=2 topologically twisted super Yang-Mills theory with gauge group SU(2) or SO(3) on compact 4-manifolds. We study the effective action in the Coulomb branch of the theory and by considering a specific Q-exact deformation to the theory we find interesting connections to mock modular forms. A specific operator of this theory computes the famous Donaldson invariants and our analysis makes their computation more accessible than previously. We also extend these ideas to the case of ramified Donaldson-Witten theory, that is the theory in the presence of embedded surfaces. Our results make calculations of correlation functions of Coulomb branch operators more trackable and we hope that they can help in the search of new 4-manifold invariants.”

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.