The Double Copy of Electric-Magnetic Duality

TL;DR

This paper reveals that the transformation linking Schwarzschild and Taub-NUT metrics is an electric-magnetic duality, connecting gravitational solutions and particle amplitudes through complex phase rotations and BMS symmetries.

Contribution

It demonstrates that the complex transformation between Schwarzschild and Taub-NUT is an electric-magnetic duality and links gravitational solutions with particle amplitudes via the double copy.

Findings

The complex transformation acts as a duality rotation at null infinity.

It relates supertranslation charges to their duals through complexification.

The phase rotation in amplitudes generates dyons from electrons.

Abstract

We argue that the complex transformation relating the Schwarzschild to the Taub-NUT metric, introduced by Talbot, is in fact an electric-magnetic duality transformation. We show that at null infinity, the complex transformation is equivalent to a complexified BMS supertranslation, which rotates the supertranslation and the dual (magnetic) supertranslation charges. This can also be seen from the cubic coupling between the classical source and its background, which for Taub-NUT is given by a complex phase rotation acting on gravitational minimal couplings. The same phase rotation generates dyons from electrons at the level of minimally coupled amplitudes, manifesting the double copy relation between the two solutions.