Kinematic Lie Algebras From Twistor Spaces

Abstract

We analyze theories with color-kinematics duality from an algebraic perspective and find that any suchtheory 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▪-algebrafeatures a kinematic Lie algebra that controls interaction vertices, both on shell and off shell. We explainthat the archetypal example of a theory with a BV▪-algebra is Chern-Simons theory, for which the resultingkinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields. TheBV▪-algebra implies the known color-kinematics duality of Chern-Simons theory. Similarly, we show thatholomorphic and Cauchy-Riemann Chern-Simons theories come with BV▪-algebras and that, on theappropriate twistor spaces, these theories organize and identify kinematic Lie algebras for self-dual and fullYang-Mills theories, as well as the currents of any field theory with a twistorial description. We show thatthis result extends to the loop level under certain assumptions