All the supersymmetric configurations of N=4,d=4 supergravity

TL;DR

This paper classifies all supersymmetric configurations of N=4, d=4 supergravity, revealing new solutions associated with timelike Killing vectors and refining existing classifications for null vectors.

Contribution

It provides a comprehensive classification of supersymmetric solutions in N=4, d=4 supergravity, including new configurations beyond previous classifications.

Findings

Classified all supersymmetric configurations maintaining S and T dualities.

Derived simple equations for classical solutions.

Discovered new solutions with timelike Killing vectors and non-trivial U(1) connections.

Abstract

All the supersymmetric configurations of pure, ungauged, N=4,d=4 supergravity are classified in a formalism that keeps manifest the S and T dualities of the theory. We also find simple equations that need to be satisfied by the configurations to be classical solutions of the theory. While the solutions associated to null Killing vectors were essentially classified by Tod (a classification that we refine), we find new configurations and solutions associated to timelike Killing vectors that do not satisfy Tod's rigidity hypothesis (hence, they have a non-trivial U(1) connection) and whose supersymmetry projector is associated to 1-dimensional objects (strings), although they have a trivial axion field.