Color-kinematics and double-copy relations for selfdual solutions

Abstract

We clarify the relation between the classical double copy and the double copy for amplitudes in the setting of selfdual gauge and gravity theories. To this end we construct explicit all-order perturbative solutions in these theories and show that they are related by a version of color-kinematics duality. This relation can be expressed in a double-copy form and embodies the most general manifestation of the selfdual classical double copy. Our classical double copy relations directly lead to known amplitude double-copy relations, both for Berends-Giele currents and on-shell amplitudes, through the perturbiner expansion.