We consider 4d N=1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robin-like. We show that different boundary conditions are related to each other by coupling the bulk to 3d N=1 degrees of freedom on the boundary three-torus, for which we derive explicit 1-loop determinants.

Semiclassical gravity is famously in tension with the unitary evolution of quantum mechanics when black holes evaporate. I'll describe a semiclassical calculation that nonetheless reproduces signatures of unitarity, namely the "Page curve" of entropy and the Hayden-Preskill protocol. This involves finding a quantum extremal surface, an extremum of the generalised entropy (the area in Planck units plus the entropy of exterior matter), which in the context of an evaporating black hole can exist far from a classical extremal surface. The calculations are performed in an exactly solvable model of Jackiw-Teitelboim gravity coupled to conformal matter. I will conclude by commenting and speculating on the implications for the information paradox.

In this talk I will discuss asymptotically AdS wormhole solutions in the context of holography. I will present how to compute correlation functions of local operators as well as non local observables such as correlation functions of Wilson loops on the distinct boundaries and I will discuss their behavior. Moreover, I will discuss the effect that multi-trace deformations have on such observables. From the computations mentioned we observe that the dual theory is expected to be described in terms of two interacting sectors coupled by a UV soft, non-local interaction. Finally, I will present a simple effective field theory construction that can explain the behaviors that we observe from these gravitational computations.

AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS space. Black holes should correspond to ensembles of states in the boundary field theory. By analyzing the superconformal index of 4d N=4 SU(N) Super-Yang-Mills, with the help of a new Bethe Ansatz type formula, we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit exhibits many competing contributions and Stokes phenomena, hinting at new physics.

Fractional quantum Hall (FQH) states are topologically ordered. Additionally, FQH states support a collective neutral excitation known as the Girvin-MacDonald-Platzman (GMP) mode. Certain features of this mode are independent of the microscopic details. The objective of the talk is to construct an effective theory includes both topological properties and the massive GMP mode. The theory reproduces the universal properties of chiral lowest Landau level (LLL) FQH states which lie beyond the TQFT data, such as the projected static structure factor and the GMP algebra of area-preserving diffeomorphisms. The dynamics of the mode is described by a fluctuating rank-2 symmetric, positive-definite tensor, which leads to a natural geometric (or gravitational) interpretation of the GMP mode.

TBA

The microstate structure of AdS3 black holes involves stringy ingredients, yet quantitative control over these ingredients in a regime where the state being described approximates a black hole has been elusive. This talk will show how 2d worldsheet current algebra provides a tool to describe the stringy objects that govern the black hole phase transition in AdS3 and linear dilaton backgrounds, providing a bridge between the entropy-carrying degrees of freedom of the dual non-gravitational theory (little strings or long strings) and their conjectured gravitational dual, the fuzzball.

I discuss the higher-derivative \alpha' corrections in the reduction to one dimension (cosmic time) that is relevant for the dynamics of cosmological backgrounds. In this setting string theory is known to be duality invariant under O(d,d), which makes it possible to completely classify all \alpha' corrections. I discuss some generic features of the \alpha' completed Friedmann equations and show that there are duality invariant theories that allow for de Sitter solutions that are non-perturbative in \alpha', suggesting that string theory may permit de Sitter vacua in this novel fashion.

We study the possibility for a unitary theory of partially-massless (PM) spin-two field interacting with Gravity in arbitrary dimensions. We show that parity invariant interactions respecting general covariance lead to a reconstruction of Conformal Gravity in even dimensions. In this case the unitarity is sacrificed. By relaxing the parity invariance, we find a possibility of a unitary theory in four dimensions, but the parity-odd cubic vertex cannot be written in usual metric variables. We comment on possible approaches that may allow for the formulation of this theory. Finally, by relaxing the general covariance, we show that a non-minimal coupling between massless and PM spin-two fields may lead to an alternative possibility of a unitary theory, that necessarily involves mixed-symmetry fields.

In this seminar I will discuss a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. We show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in detail the mechanism underlying this phenomenon and formulate a simple criterion for supersymmetry enhancement.

I review how integrability allows us to explore the planar limit of the AdS/CFT correspondence for arbitrary values of the t'Hooft coupling. In string theory integrability of the 2D σ-model is closely related to Poisson-Lie Symmetry. Double Field Theory can be used to make this symmetry manifest and therewith provides a new tool to study the implications for the gravity side of the correspondence.

We investigate holographic complexity for eternal black hole backgrounds perturbed by shock waves, with both the complexity=action (CA) and complexity=volume (CV) proposals. We consider Vaidya geometries describing a thin shell of null fluid with arbitrary energy falling in from one of the boundaries of a two-sided AdS-Schwarzschild spacetime. We demonstrate how scrambling and chaos are imprinted in the complexity of formation and in the full time evolution of complexity via the switchback effect for light shocks, as well as analogous properties for heavy ones.

Gravity theories naturally allow for edge states generated by non-trivial boundary-condition preserving diffeomorphisms. I present a specific set of boundary conditions inspired by near horizon physics, show that it leads to soft hair excitations of black hole solutions and discuss implications for black hole entropy.