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

TL;DR

We present a complete classification of all supersymmetric solutions of minimal gauged $N=2$, $D=4$ supergravity by analyzing Killing spinor bilinears. The solutions split into timelike and lightlike classes according to the norm $N=V^2$ of the Killing vector, with timelike geometries governed by a two-dimensional base and lightlike geometries described by electrovac AdS travelling waves; generically these backgrounds preserve $1/4$ of the supersymmetry. Notably, we recover the known Reissner-Nordström-Taub-Nut-AdS family and identify new Petrov type I BPS solutions in the timelike sector, while displaying a general lightlike $1/4$ BPS travelling-wave solution. The maximally supersymmetric case reduces to $AdS_4$ with vanishing gauge field, and many solutions admit uplift to eleven dimensions, enriching the landscape of BPS geometries with potential M-theory and holographic applications.

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.