Solutions of D=4 Gauged Pseudo-Supergravity

TL;DR

This paper classifies all solutions with Killing spinors in minimal anti-de Sitter N=2, D=4 supergravity with a flipped gauge kinetic term, revealing four distinct classes including gravitational waves, a new solution, fibrations, and a cosmological extension.

Contribution

It provides a comprehensive classification of solutions in gauged pseudo-supergravity using spinorial geometry, including a novel solution and new insights into solution structures.

Findings

Four classes of solutions identified

New solution corresponding to a special Killing spinor limit

Solution involving wave equations on Minkowski space

Abstract

The techniques of spinorial geometry are used to classify solutions admitting Killing spinors in the theory of minimal anti-de Sitter $N=2$, $D=4$ supergravity, where the gauge kinetic term comes with the opposite sign. There are four classes of solutions. One class is described by metrics corresponding to gravitational waves propagating on $AdS_2\times H^2$. The second class of solution is a new solution corresponding to a special limiting case of the Killing spinor. The third class of solution corresponds to fibrations over a Lorentzian three dimensional manifold which has a Lorentzian Gauduchon-Tod structure. The fourth class of solution is a cosmological extension of a Majumdar-Papapetrou type solution, described by a function satisfying the wave equation on $\mathbb{R}^{2,1}$ .