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

TL;DR

This paper constructs a Lorentz-invariant action for maximally supersymmetric self-dual Yang-Mills theory on twistor space, demonstrating its double copy to self-dual gravity and exploring the underlying algebraic structures.

Contribution

It introduces a new Lorentz-invariant action manifesting colour-kinematics duality and shows its double copy relation to self-dual gravity on twistor space.

Findings

The action manifests colour-kinematics duality.

The double copy to self-dual gravity is explicitly demonstrated.

The Hopf algebra involved is non-commutative, indicating potential for generalization.

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.