BRST-Lagrangian Double Copy of Yang-Mills Theory

Understand

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.