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.

1+19 pages, extended presentation, published version

References in corpus (10)

• New Relations for Gauge-Theory Amplitudes
• The Kinematic Algebra From the Self-Dual Sector
• A Twistorial Foundation for the Classical Double Copy
• Twistor Actions for Self-Dual Supergravities
• Kinematic Lie Algebras From Twistor Spaces
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• Isometries and the double copy
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Self-Dual Supergravity and Twistor Theory
• A spinorial double copy for $\mathcal{N}=0$ supergravity

Cited by in corpus (3)

• 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