Soft Gravity by Squaring Soft QED on the Celestial Sphere

TL;DR

The paper proposes a 2d dual-model framework on the celestial sphere to study soft S-matrices, recasting soft photon amplitudes as Coulomb gas correlators and deriving a gravity counterpart by squaring the 2d kinetic operator. This leads to a novel, unconventional double-copy-like relation between soft photon and soft graviton sectors, realized through vertex operators and a biharmonic 2d action tied to disclination physics. Ward identities in the 2d theory reproduce the soft photon and soft graviton theorems and enforce charge conservation and the equivalence principle, recasting fundamental 4d symmetries as 2d shift symmetries. The approach suggests a broader holographic, worldsheet-inspired picture of massless amplitudes at null infinity and motivates extensions to non-Abelian theories and higher-order soft theorems.

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.