Week 28.10.2024 – 03.11.2024

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.

The Landau paradigm of phase transitions states that any continuous (second order) phase transition is a symmetry breaking transition. Originally this was formulated for symmetries that form groups, e.g. the critical Ising model is the transition between the $\mathbb{Z}_2$ symmetric and spontaneously broken phases. In recent years a new class of symmetries, called categorical or non-invertible, have emerged in quantum systems -- with impact ranging from high energy and condensed matter physics to mathematics, and quantum computing. I will explain how these symmetries generalize the Landau paradigm and how new phases and phase transitions are predicted, which have potential future experimental implementations in cold atom systems.

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.

In this talk I will discuss how to deal with multi-trace operators, in particular in the context of N=4 Super Yang Mills. I will review their relevance in computing holographic correlators and discuss recent developments on how to treat them.

Amongst the most fascinating behaviours to arise from Einstein's equations is the onset of chaotic dynamics in the approach to certain cosmological singularities. This was analysed in detail in seminal work by Belinskii, Khalatnikov, Lifshitz (BKL) and others some fifty years ago. A consequence of these results is that the Schwarzschild interior solution near the singularity appears very fine-tuned and should give way for BKL-like dynamics in more generic black holes. In arxiv:2312.11622, we construct a setup that realises the so-called "mixmaster" chaotic dynamics in the interior of an AdS black hole. After reviewing the work of BKL, I will describe our holographic setup and discuss the peculiar symmetries appearing in this problem.