Soft Gravity by Squaring Soft QED on the Celestial Sphere

TL;DR

This paper explores a novel 2D topological model framework for soft $S$-matrices on the celestial sphere, revealing a double copy structure between soft photons and gravitons, and deriving fundamental principles as Ward identities.

Contribution

It introduces a new topological defect model approach to soft $S$-matrices and uncovers a classical double copy relation between gauge and gravity cases.

Findings

Reformulation of soft $S$-matrices as 2D correlation functions.

Identification of a double copy structure between photons and gravitons.

Derivation of gauge invariance and the equivalence principle as Ward identities.

Abstract

We recast the soft $S$-matrices on the celestial sphere as correlation functions of certain $2$-dimensional models of topological defects. In pointing out the double copy structure between the soft photon and soft graviton cases, we arrive at a putative classical double copy between the corresponding topological models and a rederivation of gauge invariance and the equivalence principle as Ward identities of the $2$-dimensional theories.