Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space

Abstract

We construct a simple Lorentz-invariant action for maximally supersymmetric self-dual Yang-Mills theory that manifests colour-kinematics duality. We also show that this action double copies to a known action for maximally supersymmetric self-dual gravity. Both actions live on twistor space and illustrate nicely the homotopy algebraic perspective on the double copy presented in arXiv:2307.02563. This example is particularly interesting as the involved Hopf algebra controlling the momentum dependence is non-commutative and suggests a generalisation to gauged maximally supersymmetric self-dual gravity.

arXiv comment1+19 pages, extended presentation, published version

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• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• Ambitwistor Yang-Mills Theory Revisited