S-duality and the Double Copy

TL;DR

This paper explores how S-duality in gauge theories translates into the double copy framework for gravity, connecting duality symmetries, solution transformations, and $Sl(2,R)$ actions in general relativity.

Contribution

It investigates the relationship between gauge theory dualities and gravitational solutions within the double copy formalism, extending the understanding of symmetries in gravity.

Findings

Duality symmetries in gauge theories map to solution-generating transformations in gravity.

The $Sl(2,R)$ action in general relativity relates to gauge theory dualities.

The formalism connects classical solutions in gauge theories to gravitational counterparts.

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.