Soft gravity by squaring soft QED on the celestial sphere

Abstract

We recast the soft $S$ matrices on the celestial sphere as correlation functions of certain two-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 two-dimensional theories.