BRST-Lagrangian Double Copy of Yang-Mills Theory

TL;DR

This paper demonstrates that the double copy relationship between gauge theory and supergravity extends from tree to loop levels, using BRST symmetry and field redefinitions to establish equivalence.

Contribution

It introduces a BRST-Lagrangian framework to extend the double copy construction from tree-level to loop-level in gauge theories.

Findings

Double copy extends to loop level for Yang-Mills theory.

Color-kinematic duality is linked to BRST symmetry.

Double copied action is equivalent to $ abla=0$ supergravity after field redefinitions.

Abstract

We show that the double copy of gauge theory amplitudes to $\mathcal{N}=0$ supergravity amplitudes extends from tree level to loop level. We first explain that color-kinematic duality is a condition for the Becchi-Rouet-Stora-Tyutin operator and the action of a field theory with cubic interaction terms to double copy to a consistent gauge theory. We then apply this argument to Yang-Mills theory, where color-kinematic duality is known to be satisfied onshell at tree level. Finally, we show that the latter restriction can only lead to terms that can be absorbed in a sequence of field redefinitions, rendering the double copied action equivalent to $\mathcal{N}=0$ supergravity.