Supersymmetry and Gravitational Duality

TL;DR

This paper explores how supersymmetry algebra incorporates gravitational duality by analyzing a charged Taub-NUT solution in N=2 supergravity, revealing the necessity of dual magnetic momenta in the algebra.

Contribution

It explicitly demonstrates the inclusion of dual magnetic momenta in the supersymmetry algebra through solutions and formalisms, providing new expressions for these quantities.

Findings

Dual magnetic momenta are necessary in supersymmetry algebra.

New expressions for dual magnetic momenta, including NUT charge, are derived.

Gravitational duality is consistent with supersymmetry algebra modifications.

Abstract

We study how the supersymmetry algebra copes with gravitational duality. As a playground, we consider a charged Taub-NUT solution of D=4, N=2 supergravity. We find explicitly its Killing spinors, and the projection they obey provides evidence that the dual magnetic momenta necessarily have to appear in the supersymmetry algebra. The existence of such a modification is further supported using an approach based on the Nester form. In the process, we find new expressions for the dual magnetic momenta, including the NUT charge. The same expressions are then rederived using gravitational duality.