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

Abstract

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'.

46 pages; v2: two typos corrected, acknowledgements added

References in corpus (2)

• The Duality Between Color and Kinematics and its Applications
• Deformation theory via differential graded Lie algebras

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• A new gauge-invariant double copy for heavy-mass effective theory
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• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Colour-kinematics duality, double copy, and homotopy algebras
• Perturbative Quantum Field Theory and Homotopy Algebras
• Next-to-MHV Yang-Mills kinematic algebra