New heavenly double copies

Understand

The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories.

• Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of motion can be written in a form that maps directly to Pleba\'nski's heavenly equation for self-dual gravity.
• The self-dual YM equation involves an area-preserving diffeomorphism algebra, two copies of which appear in the heavenly equation.
• In this paper, we show that this construction is a special case of a wider family of heavenly-type examples, by (i) performing Moyal deformations, and (ii) replacing the area-preserving diffeomorphisms with a less restricted algebra.