Lectures on Celestial Holography

TL;DR

This paper reviews celestial holography, showing how soft graviton theorems relate asymptotic symmetries to conformal structures on the celestial sphere, and discusses implications for scattering amplitudes.

Contribution

It provides a comprehensive overview of celestial holography, connecting soft theorems, asymptotic symmetries, and celestial amplitudes in a unified framework.

Findings

Soft graviton theorem implies Virasoro symmetry in flat space gravity

Celestial amplitudes are expressed as conformal correlators on the celestial sphere

Constraints from celestial symmetries shape scattering processes

Abstract

These notes consist of 3 lectures on celestial holography given at the Pre-Strings school 2021. We start by reviewing how semiclassically, the subleading soft graviton theorem implies an enhancement of the Lorentz symmetry of scattering in four-dimensional asymptotically flat gravity to Virasoro. This leads to the construction of celestial amplitudes as $\mathcal{S}$-matrices computed in a basis of boost eigenstates. Both massless and massive asymptotic states are recast as insertions on the celestial sphere transforming as global conformal primaries under the Lorentz SL$(2, \mathbb{C})$. We conclude with an overview of celestial symmetries and the constraints they impose on celestial scattering.