# Real Killing Spinors in Neutral Signature

## TL;DR

This paper classifies solutions with Majorana Killing spinors in 4D neutral signature supergravity, revealing two classes with distinct geometric structures and providing explicit examples of each.

## Contribution

It introduces a classification of supersymmetric solutions in neutral signature supergravity using spinorial geometry, identifying two distinct solution classes with explicit examples.

## Key findings

- Two classes of solutions preserving minimal supersymmetry are identified.
- Solutions include pseudo-hyper-Kahler and IWP-type manifolds.
- Explicit examples of each class are provided.

## Abstract

Spinorial geometry methods are used to classify solutions admitting Majorana Killing spinors of the minimal 4-dimensional supergravity in neutral signature, with vanishing cosmological constant and a single Maxwell field strength. Two classes of solutions preserving the minimal amount of supersymmetry are found. The first class admits a null-Kahler structure and corresponds to a class of self-dual solutions found by Bryant. The second class admits a null and rotation-free geodesic congruence with respect to which a parallel frame can be chosen. Examples of solutions in the former class are pseudo-hyper-Kahler manifolds; and examples in the latter class include self-dual solutions, as well as a neutral-signature IWP-type solution.