Celestial Chiral Algebras and Self-Dual Gravity

TL;DR

This paper explores celestial chiral algebras in the context of twistor theory and self-dual Einstein geometries, revealing how background geometries deform these algebras at tree level in flat space.

Contribution

It introduces tree-level deformations of celestial chiral algebras caused by non-trivial self-dual Einstein backgrounds, connecting celestial holography with twistor theory.

Findings

Derived deformations of celestial chiral algebras from self-dual geometries

Linked celestial holography to twistor theory and self-dual Einstein equations

Enhanced understanding of symmetries in flat space graviton scattering

Abstract

Celestial holography suggests, among other things, that collinear singularities of graviton scattering amplitudes are described by the OPEs of some putative dual CFT. One of the great successes has been the insight that this duality is true at tree-level which led to the discovery of new infinite dimensional symmetry algebras of tree-level amplitudes in flat space closely related to w$_{1+\infty}$. This thesis studies these celestial chiral algebras in the light of twistor theory and derives tree-level deformations thereof induced by non-trivial background geometries that solve some form of the self-dual Einstein equations.