Abstract
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.
Highlights
Published by the American Physical SocietySummation and space-time integration over repeated indices are understood
We show that the double copy of gauge theory amplitudes to N 1⁄4 0 supergravity amplitudes extends from tree level to loop level
We first explain that color-kinematics duality is a condition for the BecchiRouet-Stora-Tyutin operator and the action of a field theory with cubic interaction terms to double copy to a consistent gauge theory
Summary
Summation and space-time integration over repeated indices are understood. We are interested in theories invariant under a gauge symmetry described by a BRST operator Q. It is not hard to see that by blowing up ghost vertices in the Batalin-Vilkovisky (BV) action before gauge fixing, one can always reduce the gauge transformations of all fields to be at most cubic in the fields: QΦI qIJ ΦJ qIJK
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