In planar N=4 SYM, massless scattering amplitudes are dual to null polygonal Wilson loops (T-duality) or the same as the four-dimensional null limit of stress-tensor correlators. I will present a (conjectured) generalization of this duality which equates correlators of determinant operators, in a special ten-dimensional null limit, with massive scattering amplitudes in the Coulomb branch of N=4. This determinant operator is a generating function of all half-BPS single-traces operators. By taming it on twistor space I will show its correlators have ten dimensional poles which combine 4d space-time and 6d R-charge kinematics.

The discovery of gravitational waves has opened a new experimental window into the Universe. The fact that the relevant dynamics is often out of equilibrium offers a golden opportunity for holography to make a unique impact on cosmology and astrophysics. I will illustrate this with applications to cosmological phase transitions, to neutron star mergers and to the BKL dynamics near a cosmological singularity.

In this talk we use integrability data to bootstrap correlation functions of planar maximally supersymmetric Yang- Mills theory. Focusing on four-point correlation function of stress-tensor, we first introduce a set of sum rules that are only sensitive to single-traces in the OPE expansion (this is advantageous because this data is available from integrability). We then discuss how these sum rules can be employed in numerical bootstrap to nonperturbatively bound planar OPE coefficients. We show rigorous bounds for the OPE coefficient of the Konishi operator at various t’Hooft couplings outside the perturbative regime. The talk is based on an ongoing work and 2207.01615.

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In this talk we will discuss a new window into the solution of Heun differential equations arising in black hole perturbation theory using the tools of two-dimensional conformal field theory and gauge theories. Kerr Compton amplitudes for massless perturbation of generic spin-weight s, are written in compact form in terms of the so-called Nekrasov-Shatashvili functions; their symmetry properties are also discussed. These are then used as building blocks to study the scattering of two Kerr black holes with generic spin orientation. Comparison to conservative observables for bounded systems computed via first-order gravitational self-force methods are shown.

Next-generation gravitational-wave detectors, operating in lower frequency ranges, will explore new types of systems including fly-bys, captures, eccentric configurations and high spin, that are well described within a weak-field approximation. I will discuss our recent NLO waveform computation for black-hole scattering in the Post-Minkowskian approximation, including linear-in-spin corrections, following Ref. [2312.14859]. The result is obtained from five point one-loop scattering amplitudes including massive scalars, vectors and a graviton, and computations are performed in the numerical unitarity framework. Special emphasis is put on the treatment of the "cut term" in the observable-based approach of Kosower, Maybee and O’Connell. The result includes IR and UV divergences and I will explain their origin and their treatment to obtain a finite observable.

In this talk I will start by revisiting the calculation of entanglement entropy in free Maxwell theory in 3+1 dimensional Minkowski spacetime. I will characterize the soft sector associated with a subregion and demonstrate that conformally soft mode configurations at the entangling surface, or equivalently correlated fluctuations in the large gauge charges of the subregion and its complement, give a non-trivial contribution to the entanglement entropy across a cut of future null infinity. I will conclude with some comments on the holographic description of bulk subregions in asymptotically flat spacetimes.

Cosmological Correlators are one of the physical quantities that are of interest to cosmologists and are also of theoretical interest as they are related to CFT correlators via the AdS/CFT correspondence. These differ from the S-matrix as they are correlation functions computed on a given time slice. In this talk, I will review some progress in computing these in momentum space and also describe its relation to the S-matrix.

I will describe how to consider the flat space limit of scaterig in AdS relative to a point (where sacttering occurs). The kinematics is related to the Wigner-Inonu contraction. In particular, I will discuss how to take the proper limits of wave functions in AdS (times extra dimensions) to understand a notion of in states and out states and how a scattering amplitude should be conceived. This will make use of the embedding formalism, where the description of these wave functions is simple. I will show how these wave functions are related to other constructions in AdS/CFT and suggest how the Mellin parameters of these other setups arise from integral representations of the wave functions in terms of Schwinger parameters.

I will describe a construction relating the Vertex Operator Algebra (VOA) of a 4d N=2 superconformal field theory (SCFT) to the boundary VOA in 3d N=4 QFT, and to the VOA in 2d QFT. Besides unifying several known constructions, this also draws connections to many other interesting problems, among which are the novel rank-zero 3d N=4 SCFTs emerging in the high-temperature limit of a 4d SCFT "on the second sheet".

We propose a correspondence between topological order in 2+1d and Seifert three-manifolds together with a choice of ADE gauge group G. Topological order in 2+1d is known to be characterised in terms of modular tensor categories (MTCs), and we thus propose a relation between MTCs and Seifert three-manifolds. The correspondence defines for every Seifert manifold and choice of G a fusion category, which we conjecture to be modular whenever the Seifert manifold has trivial first homology group with coefficients in the centre of G. The construction determines the spins of anyons and their S-matrix, and provides a constructive way to determine the R- and F-symbols from simple building blocks. We explore the possibility that this correspondence provides an alternative classification of MTCs, which is put to the test by realising all MTCs (unitary or non-unitary) with rank r<=5 in terms of Seifert manifolds and a choice of Lie group G.

In this talk, I provide an improved definition of new conserved quantities derived from the energy-momentum tensor in curved spacetime by introducing an additional scalar function. I find that the conserved current and the associated conserved charge become geometric under a certain initial condition of the scalar function, and show that such a conserved geometric current generally exists in curved spacetime. Furthermore, I demonstrate that the geometric conserved current agrees with the entropy current for the perfect fluid, thus the conserved charge is the total entropy of the system.

Effective Field Theories (EFTs) allow us to describe low energy physics without knowing the specific UV completion. This comes at the cost of having free parameters (Wilson coefficients) whose values encode the UV physics, but are not constraint from a standard EFT point of view. It is well known that some values can lead to unphysical properties of these theories. In this talk, I will present a low energy technique to put bounds on these coefficients by requiring causal propagation. I will show how these bounds can be obtained in flat space and then move on to how apply these techniques in cosmological spacetimes. Throughout the talk I will present bounds on scalar and photon EFTs.

Recent years have seen an upsurge of interest in deformations of two-dimensional sigma-models which preserve classical integrability. Integrability is known to offer powerful techniques for solving such models exactly, even in complex scenarios such as at strong coupling. This talk introduces classical integrability, and the role played by worldsheet dualities in the development of a large family of integrable deformations. The second part of the talk focuses on the application of these deformations within the AdS/CFT correspondence, in order to obtain exact methods for addressing gauge and gravity theories with reduced Noether (super)symmetries. However, current "AdS/CFT integrability" methods are mostly restricted to the undeformed, maximally (super)symmetric instances. To enhance their applicability to a broader range of theoretical models, the concept of “twisted” AdS/CFT integrability is introduced, specifically targeting the “Jordanian” subclass of integrable deformations. Recent and ongoing work in this area will be discussed.

I will show how to construct a Lagrangian based on a notion of minimal coupling that includes classical spin effects that is relevant to describe Kerr binaries in the post-Minkowski (PM) regime. Using such Lagrangian, I will derive expressions for the classical amplitude for the elastic 2—>2 process at 1PM and 2PM. I will then consider radiation reaction effects and their connection to the imaginary part of the 3PM spinning eikonal phase.

From the perspective of classical gravity, a black hole is the simplest object we know of. At the same time, it possesses huge entropy, hinting at an incredibly complex microstructure: understanding this fact falls in the realm of quantum gravity. In this talk I will review recent results concerning the microscopics and the thermodynamics of the fast spinning black holes, and I will describe how recently developed techniques allow to compute the quantum corrections to the entropy of near-extremal Kerr black holes. The quantum-corrected near-extremal entropy exhibits 3/2logT behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

The quest to understand the microscopic origins of Bekenstein-Hawking entropy has been a longstanding challenge for physicists. In the context of AdS black holes, this entropy is expected to be explicable in terms of the states of the holographic dual quantum field theory, as per the AdS/CFT framework. In my talk, I will introduce the idea of gluing gravitational blocks for supersymmetric AdS black holes in String/M-theory with arbitrary rotation and generic electric and magnetic charges. This approach provides insights into the large N behavior of the partition function of the corresponding holographic dual field theory. Time permitting, I will also delve into the partition function of the 6d (2, 0) theory on S^2 x M_3, where M_3 is either a three-sphere or S^2 x S^1, and analyse its large N behaviour.

Recent developments on Feynman integrals and string amplitudes greatly benefitted from multiple polylogarithms and their elliptic analogues — iterated integrals on the sphere and the torus, respectively. In this talk, I will review the Brown-Levin construction of elliptic polylogarithms and propose a generalization to Riemann surfaces of arbitrary genus. In particular, iterated integrals on a higher-genus surface will be derived from a flat connection. The integration kernels of our flat connection consist of modular tensors, built from convolutions of Arakelov Green functions and their derivatives with holomorphic Abelian differentials. At genus one, these convolutions reproduce the Kronecker-Eisenstein kernels of elliptic polylogarithms and modular graph forms. I will conclude with an outlook on open problems and work in progress.

I will describe how various vertices and scattering amplitudes, involving background fields, probe trace anomaly coefficients in a four-dimensional (4D) renormalization group (RG) flow. Specifically, I will explain how to couple dilaton and graviton fields to the degrees of freedom of 4D QFT, ensuring the conservation of the Weyl anomaly along the RG flow for the coupled system. By providing dynamics to the dilaton and graviton fields, I will demonstrate that the graviton-dilaton scattering amplitude receives a universal contribution, exhibiting helicity flipping and being proportional to (Δc−Δa) along any RG flow. Here, Δc and Δa represent the differences in the UV and IR CFT c- and a-trace anomalies, respectively. Using a dispersion relation, (Δc−Δa) can be related to spinning massive states in the spectrum of the QFT. We test our proposal through various perturbative examples. Finally, as an application of the proposal of probing the trace anomalies using scattering amplitude, we have derived a non-perturbative bound on the UV CFT a-anomaly coefficient using numerical S-matrix bootstrap program for massive RG flow.

I will discuss our recent calculations of the observables involved in the scattering of two black holes or neutron stars at fourth post-Minkowskian order (three loops) using the Worldline Quantum Field Theory (WQFT) framework. These 4PM observables now include both spin-orbit and adiabatic tidal corrections — inclusion of the latter necessitates a renormalization of the underlying classical effective field theory (EFT). I will also explain how the Effective-One-Body (EOB) may be used to resum the observables, and provide input data for future-generation gravitational waveform models.