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.

arXiv comment23 pages, latex. References added to section 1

References in corpus (28)

• All supersymmetric solutions of minimal supergravity in five dimensions
• The Geometry of D=11 Killing Spinors
• Duality and the Signature of Space-Time
• The Geometry of D=11 Null Killing Spinors
• The spinorial geometry of supersymmetric backgrounds
• Anti-self-dual four-manifolds with a parallel real spinor
• All Supersymmetric Solutions of N=2, D=4 Gauged Supergravity
• The spinorial geometry of supersymmetric heterotic string backgrounds
• The spinorial geometry of supersymmetric IIB backgrounds
• The G_2 spinorial geometry of supersymmetric IIB backgrounds
• Kleinian Geometry and the N=2 Superstring
• All timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets
• Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity
• Systematics of M-theory spinorial geometry
• All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality
• Geometry of all supersymmetric four-dimensional $\mathcal{N}=1$ supergravity backgrounds
• Classification, geometry and applications of supersymmetric backgrounds
• (1,0) superconformal theories in six dimensions and Killing spinor equations
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Anti-Self-Dual Solutions
• All the timelike supersymmetric solutions of all ungauged d=4 supergravities
• Spinorial geometry and Killing spinor equations of 6-D supergravity
• Geometry of Killing spinors in neutral signature
• Gravitational Instantons and Euclidean Supersymmetry
• Special Geometry and Space-time Signature
• BPS Solutions of Six-Dimensional (1,0) Supergravity Coupled to Tensor Multiplets
• The structure of all the supersymmetric solutions of ungauged N = (1,0),d=6 supergravity
• Brane solitons of (1,0) superconformal theories in six dimensions with hypermultiplets

Cited by in corpus (4)

• 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