A homotopy BV algebra for Yang-Mills and color-kinematics

Understand

Yang-Mills gauge theory on Minkowski space supports a Batalin-Vilkovisky-infinity algebra structure, all whose operations are local.

• To make this work, the axioms for a BV-infinity algebra are deformed by a quadratic element, here the Minkowski wave operator.
• This homotopy structure implies BCJ/color-kinematics duality; a cobar construction yields a strict algebraic structure whose Feynman expansion for Yang-Mills tree amplitudes complies with the duality.
• It comes with a `syntactic kinematic algebra'.