Double Copy from Homotopy Algebras

TL;DR

This paper interprets the double copy construction of supergravity from Yang-Mills theory using homotopy algebras, extending previous work to loop levels and providing detailed derivations applicable to many cases.

Contribution

It introduces a homotopy algebra framework for the double copy construction, including loop-level validity and detailed derivations of the double copied Lagrangian and BRST operator.

Findings

Double copy construction interpreted via homotopy algebras.

Validation of double copy at loop level.

General applicability to various examples.

Abstract

We show that the BRST Lagrangian double copy construction of $\mathcal{N}=0$ supergravity as the `square' of Yang-Mills theory finds a natural interpretation in terms of homotopy algebras. We significantly expand on our previous work arguing the validity of the double copy at the loop level, and we give a detailed derivation of the double copied Lagrangian and BRST operator. Our constructions are very general and can be applied to a vast set of examples.