Neutral Signature Gauged Supergravity Solutions

TL;DR

This paper classifies all supersymmetric solutions of minimal D=4 gauged supergravity with (2,2) signature and positive cosmological constant that admit exactly one Killing spinor, revealing a more general geometric structure than previous classifications.

Contribution

It introduces a broader geometric framework for N=2 supersymmetric solutions in minimal D=4 gauged supergravity with (2,2) signature and positive cosmological constant.

Findings

Classified all solutions with one Killing spinor in this theory.

Identified a more general geometric structure than previous classifications.

Expressed solutions as fibrations over Lorentzian Gauduchon-Tod base spaces.

Abstract

We classify all supersymmetric solutions of minimal D=4 gauged supergravity with (2,2) signature and a positive cosmological constant which admit exactly one Killing spinor. This classification produces a geometric structure which is more general than that found for previous classifications of N=2 supersymmetric solutions of this theory. We illustrate how the N=2 solutions which consist of a fibration over a 3-dimensional Lorentzian Gauduchon-Tod base space can be written in terms of this more generic geometric structure.