Double Copy from Homotopy Algebras

Understand

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.