Locality is a powerful property of quantum field theory and implies that information can be strictly localized in regions of space, and is completely inaccessible from far away. On the other hand, the holographic nature of quantum gravity suggests that the theory is ultimately non-local and that information can never be localized deep inside some spacetime region, but rather is always accessible from the boundary. This is meant to hold as a non-perturbative statement and it remains to be understood whether quantum information can be localized within G_N perturbation theory. In this talk, I will address this problem from the point of view of the AdS/CFT correspondence. I will construct candidate local operators that can be used to localize information deep inside the bulk. They have the following two properties: they act just like standard HKLL operators to leading order at large N, but commute with the CFT Hamiltonian to all orders in 1/N. These operators can only be constructed in a particular class of states which have a large energy variance, for example coherent states corresponding to semi-classical geometries. The interpretation of these operators is that they are dressed with respect to a feature of the state, rather than to the boundary.

The Thirring Model is a covariant quantum field theory of interacting fermions, sharing many features in common with effective theories of two-dimensional electronic systems with linear dispersion such as graphene. For a small number of flavors and sufficiently strong interactions the ground state may be disrupted by condensation of particle-hole pairs leading to a quantum critical point. With no small dimensionless parameters in play in this regime the Thirring model is plausibly the simplest theory of fermions requiring a numerical solution. I will review what is currently known focussing on recent simulations employing Domain Wall Fermions (a formulation drawn from state-of-the-art QCD simulation), to faithfully capture the underlying symmetries at the critical point, focussing on the symmetry-breaking transition, the critical flavor number, and the anomalous scaling of the propagating fermion.

Using the BF formulation of JT gravity, we will extend the factorisation techniques in BF theory with compact groups to non-compact ones. The Euclidean path integral formulation of these theories provides some locality interpretation of these results in terms of gravitational edge modes. We shall comment on how to extend these ideas to 3d gravity. We will aim to stress differences occurring between gauge and gravity theories already in these low dimensional examples.

We will discuss some newly found solutions to the full massless semiclassical Einstein equation (SCE) in a cosmological setting (with Λ=0). After a short introduction to the relevant notions we present the SCE in a particular shape which allows for the construction of certain vacuum states. These states may be viewed as the least possible generalization of the Minkowski vacuum to general (cosmological) space-times. In this setting, solving the SCE breaks down into solving a certain ODE which can be approached numerically and, at least generically, we obtain solutions that well fit physical expectations. Moreover, these solutions indicate dark energy as a quantum effect back-reacting on cosmological metrics and, since in our model m=Λ=0, this may not be traced back to the usual, obvious dark-energy/cosmological constant effect of a quantum field. Also we will shortly discuss some more physical problems that can be solved by our model.

We study the four point correlator of the stress-energy tensor in N=4 SYM at leading order in inverse powers of the central charge. This corresponds to the Anti-deSitter version of the Virasoro-Shapiro amplitude. At large t'Hooft coupling lambda, we use dispersive sum rules to relate the Wilson coefficients in a 1/lambda expansion to the OPE data of heavy string operators. Assuming that the Wilson coefficients are in the ring of single valued multiple zeta values (as is expected for closed string amplitudes), we solve the dispersion relations to get the first 1/R^2 correction to the flat space amplitude.

I will present a powerful new method that for the first time allows us to compute the Kaluza-Klein spectrum of a large class of string theory compactifications, including those arising in maximal gauged supergravities and beyond. This includes geometries with little to no remaining (super-)symmetries, completely inaccessible by previous methods. I will show how these insights can be used to holographically compute the anomalous dimensions of protected and unprotected operators in strongly-coupled CFTs, as well as to study global properties of their conformal manifolds. I will also show how the method can be used to determine the perturbative stability of non-supersymmetric AdS vacua. We will see the importance of higher Kaluza-Klein modes to the physics of string compactifications, e.g. in realising the compactness of moduli spaces, restoring supersymmetry that is lost in a consistent truncation, and in destabilising non-supersymmetric vacua that appear to stable in lower-dimensional supergravities.

I will discuss the classical and quantum symmetries of TTbar-deformed CFTs and their manifestations in holography. These symmetries are infinite in number and, in a certain basis, organise into a Virasoro x Virasoro algebra with the same central charge as that of the undeformed CFT. I will present a quantum, abstract proof of the existence of these symmetries and three different explicit classical perspectives: Hamiltonian, Lagrangian and holographic. I will then discuss the relationship between the single-trace TTbar deformation and the asymptotically linear dilaton background in string theory, and show that the asymptotic symmetries of this background take an identical form to those of TTbar-deformed CFTs, further strengthening this proposed connection.

I will describe progress in formulating and solving QFT non-perturbatively in the infinite volume limit using Hamiltonian Truncation. I will present new results for time-dependent observables in a certain class of both Lagrangian and non-Lagrangian theories in 1+1d. I will also present our study of chaos and thermalization for a scalar theory, where we test the Eigenstate Thermalization Hypothesis (ETH). While we do find results which are broadly consistent with ETH, at weak coupling we also find a set of “scar” states, which do not satisfy Random Matrix Statistics, and which can be distinguished from the rest of the thermal states by the expectation value of local operators.

Carroll geometries emerge as conformal boundaries of asymptotically flat spacetimes and have come to the forefront with the advent of flat holography. I will introduce these tools and show how they are used for unravelling the boundary manifestation of Ehlers' hidden Möbius symmetry present in four-dimensional Ricci-flat spacetimes that enjoy a time-like isometry. This is achieved in a designated gauge, where the three-dimensional Carrollian nature of the null conformal boundary is manifest and covariantly implemented. The action of the Möbius group is local on the space of Carrollian boundary data. Among these data, the Carrollian Cotton tensor plays a prominent role both in the Möbius electric/magnetic duality and for the determination of charges.

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.