Gauge independent kinematic algebra of self-dual Yang-Mills theory

Abstract

The double copy programme relies crucially on the so-called color-kinematics duality which, in turn, is widely believed to descend from a kinematic algebra possessed by gauge theories. In this paper we construct the kinematic algebra of gauge invariant and off-shell self-dual Yang-Mills theory, up to trilinear maps. This structure is a homotopy algebra of the same type as the ones recently uncovered in Chern-Simons and full Yang-Mills theories. To make contact with known results for the self-dual sector, we show that it reduces to the algebra found by Monteiro and O'Connell upon taking light-cone gauge and partially solving the self-duality constraints. Finally, we test a double copy prescription recently proposed in [1] and reproduce self-dual gravity.

arXiv comment26 pages. Published version

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• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Ambitwistor Yang-Mills Theory Revisited