Becchi-Rouet-Stora-Tyutin-Lagrangian Double Copy of Yang-Mills Theory

We show that the double copy of gauge theory amplitudes to N = 0 supergravity amplitudes extends from tree level to loop level. We first explain that color-kinematics 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-kinematics duality is known to be satisfied on shell at the 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 N = 0 supergravity.

Automated summary

The paper demonstrates the double copy of gauge theory amplitudes to N = 0 supergravity amplitudes extending from tree level to loop level. The color-kinematics duality is explained to be a condition for the double copy to a consistent gauge theory, which is then applied to Yang-Mills theory where the duality is known to be satisfied on shell at tree level. It is shown that any restrictions can be absorbed through field redefinitions, making the double copied action equivalent to N = 0 supergravity.