Celestial Holography: Lectures on Asymptotic Symmetries

TL;DR

This work establishes a cohesive framework for defining and computing asymptotic symmetry groups in gauge and gravity theories with asymptotically flat boundaries, laying the foundation for celestial holography. It catalogs explicit celestial algebras in key theories—4d QED, 3d and 4d gravity, and dual scalar formulations—highlighting soft/hard decompositions, memory effects, and antipodal matching across null infinities. It then points to frontier directions, including higher-dimensional spacetimes and supersymmetric extensions (notably N=1 super-BMS3 and N=1 super-BMS4), where charges and central extensions illuminate potential celestial duals. Together, these results illuminate how soft theorems arise as Ward identities of asymptotic symmetries and chart a path toward richer celestial symmetry structures in holography.

Abstract

The aim of these Lectures is to provide a brief overview of the subject of asymptotic symmetries of gauge and gravity theories in asymptotically flat spacetimes as background material for celestial holography.

Figures (1)

• Figure 1: Penrose diagrams of Minkowski spacetime. On the left: Penrose diagram with sample light cone. Vertical curves have constant $t$ while horizontal curves have constant $r$ in standard Minkowski coordinates. The $n-2$ angular dimensions are suppressed. On the right: Massive particles travel from $i^-$ to $i^+$, whereas massless particles travel at $45^o$ incident angle between $\mathcal{I}^-$ and $\mathcal{I}^+$. Advanced ($v = t + r$) and retarded $u = t - r$ coordinates (together with angular coordinates) span the boundaries $\mathcal{I}^-$ and $\mathcal{I}^+$, respectively.BSS2021Pasterski_2019