Self-Dual Fields on Self-Dual Backgrounds and the Double Copy

TL;DR

This paper investigates the double copy correspondence for self-dual gauge and gravitational fields on self-dual backgrounds, analyzing algebraic structures and specific spacetime examples to deepen understanding of their interrelations.

Contribution

It introduces a detailed analysis of the double copy on self-dual backgrounds, including algebraic structures and explicit spacetime examples, advancing the theoretical framework.

Findings

Derived $w$-algebras for self-dual plane wave and Eguchi-Hanson spacetimes

Identified modified Poisson structures in self-dual backgrounds

Analyzed the impact of gauge-fixing conditions on the double copy

Abstract

We explore the double copy for self-dual gauge and gravitational fields on self-dual background spacetimes. We consider backgrounds associated to solutions of the second Plebanski equation and describe results with different gauge-fixing conditions. Finally we discuss the kinematic and $w$-algebras and the double copy, identifying modified Poisson structures and kinematic structure constants in the presence of the self-dual background. The self-dual plane wave and Eguchi-Hanson spacetimes are studied as examples and their respective $w$-algebras derived.