Real Killing Spinors in Neutral Signature

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.

23 pages, latex. References added to section 1

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• Hypersymplectic Geometry and Supersymmetric Solutions in (t,s) 5D Supergravity
• Type-II Calabi-Yau compactifications, T-duality and special geometry in general spacetime signature
• Supersymmetry algebras in arbitrary signature and their R-symmetry groups
• Neutral Signature Gauged Supergravity Solutions