A double copy for asymptotic symmetries in the self-dual sector

TL;DR

This paper develops a double copy framework for asymptotic symmetries in the self-dual sectors of Yang-Mills and gravity, revealing novel non-perturbative rules and connections to BMS symmetries at null infinity.

Contribution

It introduces a double copy construction for symmetries in self-dual Yang-Mills and gravity, including new non-perturbative rules and the identification of YM origins of extended BMS symmetries.

Findings

Infinite set of double copy constructible symmetries identified.

Novel non-perturbative double copy rules in the bulk.

YM origin of extended BMS symmetries at null infinity.

Abstract

We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side. At null infinity, we find the YM origin of the subset of extended Bondi-Metzner-Sachs (BMS) symmetries that preserve the self-duality condition. In particular, holomorphic large gauge YM symmetries are double copied to holomorphic supertranslations. We also identify the single copy of superrotations with certain non-gauge YM transformations that to our knowledge have not been previously presented in the literature.