Abstrakt
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.