BRST-Lagrangian Double Copy of Yang-Mills Theory

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 explainthat color-kinematic duality is a condition for the Becchi-Rouet-Stora-Tyutinoperator and the action of a field theory with cubic interaction terms todouble copy to a consistent gauge theory. We then apply this argument toYang-Mills theory, where color-kinematic duality is known to be satisfiedonshell at tree level. Finally, we show that the latter restriction can onlylead to terms that can be absorbed in a sequence of field redefinitions,rendering the double copied action equivalent to $\mathcal{N}=0$ supergravity