Kinematic Lie Algebras from Twistor Spaces.

We analyze theories with color-kinematics duality from an algebraic perspective and find that any such theory has an underlying BV^{▪}-algebra, extending the ideas of Reiterer [A homotopy BV algebra for Yang-Mills and color-kinematics, arXiv:1912.03110.]. Conversely, we show that any theory with a BV^{▪}-algebra features a kinematic Lie algebra that controls interaction vertices, both on shell and off shell. We explain that the archetypal example of a theory with a BV^{▪}-algebra is Chern-Simons theory, for which the resulting kinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. The BV^{▪}-algebra implies the known color-kinematics duality of Chern-Simons theory. Similarly, we show that holomorphic and Cauchy-Riemann Chern-Simons theories come with BV^{▪}-algebras and that, on the appropriate twistor spaces, these theories organize and identify kinematic Lie algebras for self-dual and full Yang-Mills theories, as well as the currents of any field theory with a twistorial description. We show that this result extends to the loop level under certain assumptions.

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.