The talk summarises recent work that illuminates our understanding of black hole entropy for supersymmetric black holes in Anti-de-Sitter space. We consider supersymmetric $AdS_3\times Y_7$ solutions of type IIB and $AdS_2\times Y_9$ solutions of $D=11$ supergravity. These can arise as the near horizon limit of black strings in $AdS_5$ and and black holes in $AdS_4$ spacetimes, respectively. We explain how novel extremisation techniques enable one to compute physical observables without explicitly solving Einstein equations. This allows one to identify infinite new classes of $AdS_3$/d=2 SCFT pairs, as well obtain a microstate counting interpretation for infinite classes of supersymmetric black holes in $AdS_4$. A sub-class of examples correspond to branes wrapping certain two-dimensional orbifolds known as spindles and this has opened up a new direction in AdS/CFT with novel connections to accelerating black holes.

Local Schur operators in 4d N=2 SCFTs form a protected class of operators giving rise to a 2d vertex operator algebra. Following the local operator picture, we introduce classes of conformal extended operators (lines, surfaces) and study these in twisted Schur cohomology. We show how these operators support a more general algebraic structure compared to the local operators, giving rise to an extension of the vertex algebra known for local Schur operators.

Chern-Simons (CS) theory provides an attractive framework for quantizing 3d gravity, at least around a fixed saddle-point. But how do we describe matter in CS gravity while retaining its useful features? In this talk I will focus on the CS description of Euclidean de Sitter space about its three-sphere saddle. I will introduce a "Wilson spool," which can be interpreted as a collection of Wilson loops winding arbitrarily many times around the three-sphere and which provides an effective description of massive one-loop determinants. Constructing and subsequently evaluating the spool will require us to revisit starting assumptions about unitarity of the representations appearing in the Wilson loops as well as the library of "exact methods" available to CS theories on the three-sphere. The result will be an object that reduces to the scalar one-loop determinant on the three-sphere in the limit that Newton's constant vanishes yet can be evaluated at in any order in G_N perturbation theory. Time remaining, I will either discuss potential further applications of the Wilson spool (either to spinning fields or to contexts outside of de Sitter) or (unresolved) implications of CS gravity for the dS/CFT dictionary.

Higher-spin gravity is a curious beast of mathematical physics: a cousin of supergravity and string theory that seems comfortable with 4 spacetime dimensions and positive cosmological constant. On the other hand, general arguments show that this theory must be pathologically non-local at quartic order. In this talk, I claim that the non-locality arguments rely on Lorentzian boundary signature. For Euclidean boundary, explicit calculation shows that the feared non-locality is absent. This implies that the theory is healthy in de Sitter space, but not in (Lorentzian) AdS. The surprising possibility of such signature-dependent locality has long been implicit in the CFT/holography literature. Higher-spin gravity provides the first explicit example.

Nonintegrable QFTs are expected to thermalize and exhibit emergence of hydrodynamics and chaos. In weakly coupled QFTs, kinetic theory captures local thermalization; such a versatile tool is absent away from the perturbative regime. I will present analytical and numerical results using nonperturbative methods to study thermalization at strong coupling. I will show how requiring causality in the thermal state leads to strong analytic constraints on the thermodynamics and out-of-equilibrium properties of any relativistic 1+1d QFT. I will then discuss Lightcone Conformal Truncation (LCT) as a powerful numerical tool to study thermalization of QFTs. Applied to \phi^4 theory in 1+1d, LCT reveals eigenstate thermalization and onset of random matrix universality at any nonzero coupling. Finally, I will discuss prospects for observing the emergence of hydrodynamics in QFTs using Hamiltonian truncation. (Based on: https://arxiv.org/abs/2207.11261 and https://arxiv.org/abs/2105.02229).

In this talk, I will discuss the dynamical consequences of having 1-form and 2-group symmetries in Argyres-Douglas (AD) theories, particularly focusing on D_p(G) theories. I will first review how to construct (G,G') and D_p(G) theories from geometric engineering. Then, I will briefly review how 1-form symmetries are found in these AD theories, focusing on their dynamical consequences in the study of the Higgs branch for such theories. Analogously, I will show how certain D_p(G) theories enjoy a 2-group structure due to a non-trivial extension between a discrete 1-form symmetry and a continuous 0-form symmetry, emphasizing the dynamical consequences that a 2-group structure entails, and the family of AD theories that have it. If time permits it, I will show that it is possible to obtain an infinite family of AD theories starting from an arbitrary D_p(G) theory, where the theories in the same family share some properties. We called this "bootstrapping" of D_p(G) theories. The bootstrapping is also visible at the level of the 3d mirror theories of the D_p(G). My results are based mainly on arXiv:2203.16550 [hep-th] and arXiv:2208.11130 [hep-th].

We describe the dynamical evaporation of a black hole as the classical evolution in time of a black hole in an Anti-de Sitter braneworld. A bulk black hole whose horizon intersects the brane yields the classical bulk dual of a black hole coupled to quantum conformal fields. The evaporation of this black hole happens when the bulk horizon slides off the brane, making the horizon on the brane shrink. We use a large-D effective theory of the bulk Einstein equations to solve the time evolution of these systems. With this method, we study the dual evaporation of a variety of black holes interacting with colder radiation baths. We also obtain the dual of the collapse of holographic radiation to form a black hole on the brane.

In this talk, we will give an overview of the recent developments on the spin chains encoding the spectral problem of four dimensional N=2 superconformal gauge theories.

I will describe a method for approximately solving the crossing equations in a general CFT, using Reinforcement Learning as a stochastic optimiser. I will then present an application of this approach in the context of the 6D (2,0) theory

The worldsheet theory of string backgrounds is a CFT with zero central charge. This is the definition of on-shell string theory. In off-shell string theory, on the other hand, conformal invariance on the worldsheet is explicitly broken, and the worldsheet theory is therefore a QFT rather than a CFT, with a UV cutoff. In the first part of the talk, I will explain Tseytlin’s prescriptions for constructing classical (tree-level) off-shell effective actions and provide a general proof, using conformal perturbation theory, that it gives the correct equations of motion, to all orders in perturbation theory and α′. I will also show how Tseytlin's prescriptions are equivalent to quotienting out by the gauge orbits of a regulated moduli space with "n" operator insertions. In the second part of the talk, I will explain the underlying conceptual structure of the Susskind and Uglum black hole entropy argument. There I will show how the classical (tree-level) effective action and entropy S = A/4G_N can be calculated from the sphere diagrams. Time permitting, I will also discuss ongoing work for deriving the holographic entanglement entropy (the RT formula) in AdS3/CFT2. I will end with mentioning some important insights into how the ER=EPR hypothesis can be implemented using tachyon condensation on orbifolds in string theory.

After reviewing different aspects of thermalization and chaos in holographic quantum systems, I will argue that universal aspects can be captured using an effective field theory framework that shares similarities with hydrodynamics. Focusing on the quantum butterfly effect, I will explain how to develop a simple effective theory of the 'scramblon' from path integral considerations. I will also discuss applications of this formalism to shockwave scattering in black hole backgrounds in AdS/CFT.

Line defects play an important role in our understanding of QFTs, explaining interesting phenomena in both condensed matter physics and high-energy theories, and giving access to new data and observables. I will discuss recent work in which we explore 1d conformal line defects with an additional O(2) symmetry using the numerical bootstrap. The starting point is an agnostic approach, where we perfom a systematic bootstrap study of correlation functions between two canonical defect operators: the displacement and the tilt. We then move on to study two specific defects: a monodromy line defect and a localized magnetic field line defect. I will highlight the results of the latter one, where we found a series of intriguing cusps which we investigate.

According to the correspondence principle, classical physics emerges in the limit of large quantum numbers. We examine two examples of the semiclassical description of conformal field theory data: large spin impurities in the free triplet scalar field theory and large charge Wilson lines in QED. By simultaneously taking the coupling to zero and quantum numbers to infinity, we can connect the microscopic to the emergent classical description smoothly.

The search for pragmatic observables of quantum gravity remains at the forefront of fundamental physics research. A large set of ideas collectively known as the gauge-gravity duality have proven fruitful in tackling this problem. While such a duality is believed to universally govern gravitational theories, its nature in theories of gravity that describe our universe to a good degree of approximation is still little understood. In this talk I will discuss efforts in formulating a holographic correspondence for gravity in four-dimensional asymptotically flat spacetimes. The proposed dual theory lives on a two-dimensional celestial sphere at infinity and is constrained by a wide range of symmetries. I present recent evidence for this proposal by showing that it arises naturally in a flat space limit of AdS/CFT. I will illustrate this construction with two related examples: the propagation of a particle in a shockwave background and the high-energy scattering of 2 particles.

I will discuss the two-dimensional O(n) model for a continuous range of n. It can be defined non-perturbatively for any n as an infrared limit of certain lattice loop models, which in the IR give rise to two families of CFTs. For n<2 these CFTs are logarithmic, while for n>2 they are also complex. For n<2 the RG flow to the fixed points violates the straightforward notion of naturalness and appears tuned.

I will present an ongoing work on an integrable long-range deformation of the XXZ spin chain which can also be seen as a quantum deformation of the Haldane-Shastry model. At generic values for the deformation parameter, the model possess quantum affine symmetry, but when q is root of unity we expect extra symmetries to occur. We are studying the case q=i, which in the nearest neighbour case is solvable by the Jordan-Wigner transformation. The long-range case is also reducible to a fermionic long-range model. I will discuss the main characteristics of the model, which are very different for the even and odd number of sites.

Boundary critical behaviours of systems at bulk criticality have been studied by condensed matter physicists for decades, in the beginning mostly theoretically, then also experimentally. These studies have revealed that the field of boundary critical phenomena is quite rich. For any universality class of bulk critical behaviour usually several distinct universality classes of boundary critical behaviour exist. To elucidate this, we introduce appropriate lattice models and map them onto boundary field theories describing their scale and conformal invariance on large scales. We show that this mapping can be subtle in some cases. We discuss the role and difference of boundary conditions of the field theories on mesoscopic and large scales, to what extent they are characteristic of --- and hence may be used to identify --- the distinct boundary universality classes. Finally, we explain the characteristic near-boundary asymptotic behaviours they exhibit and mention some open problems.

Fracton phases are characterized by their elementary excitations having restricted mobility, and have recently been of relevance in several subjects, from quantum information to thermalization, from gravity to elasticity. In the context of hydrodynamics it has been shown theoretically, and confirmed experimentally, that such restricted mobility leads to novel emergent scaling laws. In this talk, I will introduce a framework to describe the hydrodynamics of fractons and predict such scaling laws, with particular focus on systems with conserved dipole and momentum. This hydrodynamics turns out to have rather exotic properties, owing to the fact that dipole conservation leads to a non-trivial extension of spacetime symmetries. After developing an effective theory approach that allows accounting for fluctuations, I will show that such theory contains relevant nonlinearities that lead to the emergence of stochastic non-Gaussian universality classes, even in three spatial dimensions, thus constituting a breakdown of its local hydrodynamic description.

The Schwinger model is one of the simplest gauge theories, yet it is only solvable in the massless case. In order to obtain numerical results, the Kogut-Susskind lattice approach with staggered fermions is regularly used. I will show that, contrary to what it was believed, the lattice mass and the continuum mass are actually not the same, but they are related by a mass shift. This can be understood by considering the (anomalous) chiral symmetry in the massless case, and has the advantage of greatly improving convergence of the numerics. I will comment on the charge-q Schwinger model as well as the multiflavor Schwinger model.