Entanglement entropy in quantum field theory is UV-divergent, which makes it a challenging quantity to analyze from an algebraic perspective. In this talk, I will describe how perturbatively coupling to gravity improves this situation, resulting in a well-defined notion of renormalized entropy in the semiclassical limit. This entropy is constructed using techniques from the theory of von Neumann algebras, and agrees with the generalized entropy of a subregion, consisting of the sum of the quantum field entanglement entropy and the area of the entangling surface. As an application, I will show how to derive the generalized second law for black hole horizons in terms of this renormalized entropy. Time permitting, I will also discuss a construction of a gravitational von Neumann algebra in a slow-roll inflation background, and describe how the background provides an intrinsic notion of a cosmological observer.

I will revisit the problem of defining an invariant notion of brane tension, analogous to the ADM mass, in a theory of gravity. I will propose two natural definitions, a gravitational and an inertial tension, in terms of asymptotic data akin to that of a Defect CFT. I will illustrate these definitions with various examples, and present the evidence why for supersymmetric branes the two tensions must be equal.

Flat space admits a foliation by AdS leaves. One seeks to derive the bulk to boundary dictionary for flat space holography as the uplift of the AdS/CFT dictionary.Over the last year progress on this front has been made by isolating the contribution to bulk amplitudes associated to a single AdS leaf. This has culminated in the construction of a 2D leaf CFT, consisting of a Liouville field, a level one current algebra and a weight -3/2 fermion, which reproduces the bulk tree MHV gluon amplitude. This talk will review these developments.

The numerical S-matrix Bootstrap aims at establishing non-perturbative universal bounds on physical observables that can be extracted from scattering amplitudes in any dimension. In the first part of the talk, I will review our past explorations of the space of supergravity amplitudes and their connection to String/M theory. I will discuss the universal bounds on the first non-universal correction to sugra amplitudes, and how the extremal solution is compatible with clustering in the Born regime, and with the Quantum Regge growth hypothesis. In the second part of the talk I will report on a first Bootstrap exploration of multi-particle scattering. I will focus on the simplest non-integrable S-matrix describing the scattering of branons on the world-sheet of confining strings in three dimensions.

In this talk, I will show how one can study gravitational perturbations from the near-horizon region of extremal and near-extremal rotating black holes in a general higher-derivative extension of Einstein gravity. I will explain how the near-horizon Teukolsky equation is modified via a correction to the angular separation constant. The near-horizon region also provides constraints on the form of the full modified Teukolsky radial equation, which serve as a stepping stone towards the study of quasinormal modes of near-extremal black holes. In the second part of the talk, I will present a new family of EFT, motivated by preserving two fundamental properties of GR: gravitational waves are non-birefringent, and black hole quasinormal modes are isospectral. This leads to a novel class of EFT extensions, which remarkably, coincides with predictions from string theory and implies a previously unknown feature of string theory effective actions.

Black holes in AdS$_d$ ($d \geq 4$) are always unstable at large angular momentum and sometimes unstable at large charge. We present proposals for the end points of these instabilities. Our constructions suggest new entropy formulae for ${\cal N}=4$ Yang Mills theory for a range of charges around extremality, and in particular for those that saturate the BPS bound.

We demonstrate that crossing symmetry of S-matrices can be violated in theories with non-invertible symmetries. Focusing on integrable flows to gapped phases in two dimensions, we show that S-matrices derived previously from the bootstrap approach are incompatible with non-invertible symmetries along the flow. We present consistent alternatives, which however violate crossing symmetry and obey modified rules dictated by fusion categories. We also show how these modified crossing rules can be used to constrain the space of amplitudes with a given categorical symmetry.

How are bulk strings related to boundary Feynman diagrams? I will give an overview of my work with Rajesh Gopakumar on deriving the closed string dual to the simplest possible gauge theory, a Hermitian matrix integral. Working in the conventional 't Hooft limit, we extract topological string theories which replace the minimal string away from the double-scaling limit. We show how to exactly reconstruct both the closed string worldsheet and its embedding into the emergent target space, purely from the matrix Feynman diagrams. I'll close by embedding our results in the broader context of AdS/CFT.

It is by now well understood how leading soft theorems follow as Ward identities of asymptotic symmetries defined at null infinity. For subleading infrared effects the connection is more subtle, but it turns out that this can be formalised, to all orders in the energy expansion, by adapting the Stuckelberg procedure to construct an extended radiative phase space at null infinity. I will exemplify this with Yang-Mills theory, showing the construction of the extended phase space, as well as the charges corresponding to the subleading soft theorems at all orders. These turn out to satisfy simple recursion relations, and organise themselves into infinite dimensional algebras in certain subsectors.

We use a relative entropy in order to establish the irreversibility of renormalization group flows on planar d-dimensional defects, embedded in D-dimensional conformal field theories. This proof completes and unifies all known defect irreversibility theorems for defect dimensions d≤ 4. The F-theorem on defects (d= 3) is a new result using information-theoretic methods.

In a very general setting, entropy quantifies the amount of information about a system that an observer has access to. However, in contrast to quantum mechanics, in quantum field theory naive measures of entropy are divergent. To obtain finite results, one needs to consider measures such as relative entropy, which can be computed from the modular Hamiltonian using Tomita--Takesaki theory. In this talk, I will give a short introduction to Tomita--Takesaki modular theory and present examples of modular Hamiltonians. Using these, I will give results for therelative entropy between the de Sitter vacuum state and a coherent excitation thereof in diamond and wedge regions, and show explicitly that the result satisfies the expected properties for a relative entropy. Finally, I will use local thermodynamic laws to determine the local temperature that is measured by an observer, and consider the backreaction of the quantum state on the geometry to prove an entropy-area law for de Sitter spacetime. Based on arXiv:arXiv:2308.14797, 2310.12185, 2311.13990 and 2312.04629.

In this talk, I will employ an ADM deparametrization strategy to discuss the radial canonical formalism of asymptotically AdS_3 gravity. It leads to the identification of a radial 'time' before quantization, namely the volume time, which is canonically conjugate to York time. Holographically, this allows to interpret the semi-classical partition function of TTbar theory as a Schrodinger wavefunctional satisfying a Schrodinger evolution equation in volume time. The canonical perspective can be used to construct from the Hamilton-Jacobi equation the BTZ solution, and corresponding semi-classical Wheeler-DeWitt states. Based on upcoming work with Matthew J. Blacker, Blanca Hergueta and Sirui Ning.

I will show how to calculate 1/N expansion of the vacuum energy of the 2D SU(N) Principal Chiral Model for a certain profile of chemical potentials. Combining this expansion with strong coupling I will identify double-scaling limit which bears striking similarities to the c = 1 non-critical string theory and suggests that the double-scaled PCM is dual to a non-critical string with a (2 + 1)-dimensional target space where an additional dimension emerges dynamically from the SU(N) Dynkin diagram. Developing this idea further, I will show how to solve large-N PCM for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an asymptotically free QFT. The solution matches one-loop perturbative calculation at weak coupling, and in the opposite strong-coupling regime exhibits an emergent spacial dimension from the continuum limit of the SU(N) Dynkin diagram. In the second part of my talk I will show that the calculation of the expectation value of half-BPS circular Wilson loops in N = 2 superconformal A_{n−1} quiver gauge theories trivialises in the large n limit (similarly to PCM), construct 1/n expansion, identify DS limit and solve it for any finite value of DS parameter and any profile of coupling constants.

I will be using scattering amplitudes, instead of the Lagrangian of General Relativity (GR), to compute classical observables in GR. In the first part of the seminar I will consider the elastic scattering of two massive particles, describing two black holes, and I will show how to compute the eikonal up to two-loop order, corresponding to third Post-Minkowskian (3PM) order, that contains all the classical information. From it I will compute the first observable that is the classical deflection angle. In the second part of the seminar I will consider inelastic processes with the emission of soft gravitons. In this case the eikonal becomes an operator containing the creation and annihilation operators of the gravitons. The case of soft gravitons can be treated following the Bloch-Nordsieck approach and, in this case, I will be computing two other observables: the zero-frequency limit (ZFL) of the spectrum dE/d\omega of the emitted radiation and the angular momentum loss at 2PM and 3PM. I will consider also the case in which there are static modes localised at $\omega=0$. In the third part of the seminar I will be discussing soft theorems with one graviton emission, first briefly at tree level, and then at loop level following the paper by Weinberg from 1965. Assuming the eikonal resummation and that all infrared divergences in the case of gravity come only from one loop diagrams, I will compute the universal soft terms, corresponding to $\frac{1}{\omega}$, $\log \omega$ and $\omega \log^2 \omega$, first at the tree and one-loop level and then for the last two observables also at two-loop level. I will then use them to compute their contribution to the spectrum of emitted energy. Finally, if I have time left, I I will study the high energy limit. In particular, since the graviton is the massless particle with the highest spin, we expect universality at high energy. I will show that universality at high energy is satisfied both in the elastic and inelastic case, but this happens in the inelastic case in a very non trivial way. I will end with some conclusions and with a list of open problems.

I will introduce a first-order formalism for two-dimensional sigma models with the Kähler target space. I will explain how to compute the metric beta function in this approach using the conformal perturbation methods. Comparing the answer with the standard geometric background field methods we observe certain anomalies, which we later resolve with supersymmetric completion. Based on 2312.01885 and 2307.04665.

3d mirror symmetry for theories with eight supercharges is understood in terms of Hanany-Witten brane setups and plays an important role in many areas of supersymmetric qft’s. The generalization to theories with four supercharges, in the non-Abelian case, has been a long standing open problem. In this talk, based on work with Riccardo Comi and Sara Pasquetti, we focus on brane setups with NS and D5’ branes, proposing that the related quiver gauge theories involve ‘improved bifundamentals’, that is strongly coupled SCFT's which are ancestors of the well known T[SU(N)] theories. Our proposal leads to 3d mirror dualities that can be exactly proven, reducing them to known Seiberg-like dualities. This gives strong support to the proposal. The simplest example is the duality between adjoint SQCD with F flavors, and a quiver with F-1 nodes and F-2 improved bifundamentals.

Euclidean wormholes are exotic types of gravitational solutions that still challenge our physical intuition and understanding. After reviewing universal properties of asymptotically AdS wormhole solutions from a gravitational (bulk) point of view and the paradoxes they raise, I will describe some concrete (microscopic) field theoretic setups and models that exhibit such properties. These models can be reduced to matrix integrals and crucially involve correlated ("entangled") sums of representations of the boundary symmetry group. I will conclude with the realisation of such set-up in N=4 SYM/type IIB SUGRA.

We propose the Gauge Theory Bootstrap, a method to compute the pion S-matrix that describes the strongly coupled low energy physics of QCD and other similar gauge theories. The method looks for the most general S-matrix that matches at low energy the tree level amplitudes of the non-linear sigma model and at high energy, QCD sum rules and form factors. We compute pion scattering phase shifts for all partial waves with angular momentum $\ell<=3$ up to 2 GeV and calculate the low energy ChiPT coefficients. This is a theoretical/numerical calculation that uses as only data the pion mass $m_\pi$, pion decay constant $f_{\pi}$ and the QCD parameters $N_c=3$, $N_f=2$, $m_q$ and $\alpha_s$. All results are in reasonable agreement with experiment. In particular, we find the $\rho(770)$, $f_2(1270)$ and $\rho(1450)$ resonances and some initial indication of particle production near the resonances. The interplay between the UV gauge theory and low energy pion physics is an example of a general situation where we know the microscopic theory as well as the effective theory of long wavelength fluctuations but we want to solve the strongly coupled dynamics at intermediate energies. The bootstrap builds a bridge between the low and high energy by determining the consistent S-matrix that matches both and provides, in this case, a new direction to understand the strongly coupled physics of gauge theories. Based on work with Martin Kruczenski.