The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets

TL;DR

This paper classifies all supersymmetric solutions in ungauged N=2, d=4 supergravity with vector multiplets, identifying conditions for solutions like black holes, pp-waves, and cosmic strings based on Killing vector properties.

Contribution

It provides a complete classification of supersymmetric configurations, distinguishing between timelike and null classes, and clarifies their relation to known solutions.

Findings

Timelike class includes known supersymmetric black holes.

Null class encompasses pp-waves and cosmic strings.

Conditions for solutions to satisfy equations of motion are specified.

Abstract

We classify all the supersymmetric configurations of ungauged N=2,d=4 supergravity coupled to n vector multiplets and determine under which conditions they are also classical solutions of the equations of motion. The supersymmetric configurations fall into two classes, depending on the timelike or null nature of the Killing vector constructed from Killing spinor bilinears. The timelike class configurations are essentially the ones found by Behrndt, Luest and Sabra, which exhaust this class and are the ones that include supersymmetric black holes. The null class configurations include pp-waves and cosmic strings.