All Supersymmetric Solutions of N=2, D=4 Gauged Supergravity

TL;DR

This paper classifies all supersymmetric solutions in minimal gauged supergravity in four dimensions, revealing new solutions and structures, including electrovac AdS waves and Petrov type I geometries, with implications for higher-dimensional theories.

Contribution

It provides a complete classification of supersymmetric solutions in N=2, D=4 gauged supergravity, including new solutions of Petrov type I and electrovac AdS waves.

Findings

Solutions are classified into timelike and lightlike classes.

New Petrov type I BPS solutions are found in the timelike case.

Electrovac AdS travelling wave solutions are identified in the lightlike case.

Abstract

We classify all supersymmetric solutions of minimal gauged supergravity in four dimensions. There are two classes of solutions that are distinguished by the norm of the Killing vector constructed from the Killing spinor. If the Killing vector is timelike, the solutions are determined by the geometry of a two-dimensional base-manifold. When it is lightlike, the most general BPS solution is given by an electrovac AdS travelling wave. This supersymmetric configuration was previously unknown. Generically the solutions preserve one quarter of the supersymmetry. Also in the timelike case we show that there exist new BPS solutions, which are of Petrov type I, and are thus more general than the previously known type D configurations. These geometries can be uplifted to obtain new solutions of eleven-dimensional supergravity.