S-duality and the Double Copy

TL;DR

The paper investigates non-perturbative dualities in the gauge-gravity double copy, showing how electromagnetic duality in the gauge theory doubles to a gravity solution-generating symmetry, namely the Ehlers transformation, within an $SL(2,\mathbb{R})$ structure. It develops and contrasts two complementary non-perturbative frameworks—the Kerr-Schild and Weyl double copy—and demonstrates their consistency across Schwarzschild, Taub-NUT, Type D, and Eguchi-Hanson spacetimes. The authors show that Buchdahl's reciprocal transformation corresponds to charge conjugation on the gauge side, while the Ehlers group induces electromagnetic duality rotations and charge rearrangements that preserve the double copy. The discussion extends to higher dimensions and emphasizes the role of hidden symmetries, the principal tensor, and the potential for a broader, non-perturbative understanding of the double copy in gravity.

Abstract

The double copy formalism provides an intriguing connection between gauge theories and gravity. It was first demonstrated in the perturbative context of scattering amplitudes but recently the formalism has been applied to exact classical solutions in gauge theories such as the monopole and instanton. In this paper we will investigate how duality symmetries in the gauge theory double copy to gravity and relate these to solution generating transformations and the action of $Sl(2,R)$ in general relativity.