Self-Dual Fields on Self-Dual Backgrounds and 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.