Week 14.10.2024 – 20.10.2024

These lectures will review recent developments surrounding the infrared sector of gravity in (3+1)-dimensional asymptotically flat spacetimes (AFS). In the first part of the course we will introduce soft theorems which govern the low-energy scattering of massless particles such as photons and gravitons. We will explain how these are related to classical observables known as memory effects and discuss their application to computing infrared-finite collider observables and gravitational waveforms. In the second part, we will introduce the notion of asymptotic or large-gauge symmetries and use it to derive the infinite-dimensional asymptotic symmetry algebra of (3+1)-dimensional AFS, also known as the BMS algebra. We will show that the conservation laws associated with these symmetries are equivalent to the Weinberg soft graviton theorem. Time-permitting, we will discuss some implications of these ideas for non-AdS holography.

In recent years we've expanded our understanding of entanglement in many-body quantum systems; both how it behaves in ground states, and how it grows out-of-equilibrium. Entanglement is very difficult to measure in experiments. But through understanding it better, we've made great progress in classifying quantum phases of matter, and in developing algorithms for efficiently simulating quantum systems. I will review some recent progress in these directions.

In the first part of the talk I will recap the black hole thermodynamics of a certain non-supersymmetric asymptotically AdS_5 black hole: I will define its asymptotic charges and associated potentials and show some thermodynamic relations between them. Then I will describe the so-called BPS point, where the black hole is extremal (zero temperature) and supersymmetric. Finally, I will show how to approach the vicinity of the BPS point, without exactly landing on it and discuss the significance of this near-BPS limit and its relation to the Schwarzian mode. In the second part of the talk, I will introduce the holographically dual 4d field theory and describe its basic properties. In particular, I will describe how the supersymmetry breaking (which occurred on the gravity side) can be kept under control on the field theory side. Finally, I will present a preliminary calculation providing a match between the classical gravity partition function and the classical field theory partition function in this thermal setting.

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.