Real Supersymmetric Solutions of (3,2) Signature Five-Dimensional Supergravity

TL;DR

This paper classifies supersymmetric solutions in five-dimensional (3,2) signature supergravity, revealing geometric structures and constructing explicit solutions, including novel N=6 supersymmetric configurations absent in standard signatures.

Contribution

It provides a complete classification of supersymmetric solutions in (3,2) signature supergravity and introduces new solutions with higher supersymmetry not seen in standard cases.

Findings

Solutions characterized by a nilpotent integrable endomorphism.

Constructed supersymmetric domain wall solutions linked to Killing-Yano 2-forms.

Discovered a new N=6 supersymmetric descendant preon solution.

Abstract

We classify supersymmetric solutions of D=5 (3,2) signature supergravity with either vanishing or imaginary gauge coupling constant preserving the minimal N=2 supersymmetry. We prove that the geometry of such solutions is characterized by a nilpotent integrable endomorphism, and obtain the necessary and sufficient conditions on the fluxes imposed by supersymmetry. We also construct examples of supersymmetric domain wall solutions for which the nilpotent integrable endomorphism is associated with a Killing-Yano 2-form, as well as a new descendant preon solution which preserves N=6 supersymmetry. This is notable as such N=6 descendant solutions do not exist in the standard signature D=5 supergravity.