On supersymmetric Einstein-Weyl spaces

Abstract

We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor, implies the geometry to be Einstein-Weyl. We then use techniques developed for the classification of supersymmetric solutions to supergravity theories to characterise those Lorentzian EW geometries that allow for a weighted parallel spinor, calling the resulting geometries supersymmetric. The overall result is that they are either conformally related to ordinary geometries admitting parallel spinors (w.r.t. the Levi-Civita connection) or are conformally related to certain Kundt spacetimes. A full characterisation is obtained for the 4 and 6 dimensional cases.

17 pages, version to be published in JGP

References in corpus (9)

• Kundt Spacetimes
• General Kundt spacetimes in higher dimensions
• HKT Geometry and de Sitter Supergravity
• Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
• Supersymmetry, holonomy and Kundt spacetimes
• Solutions of Minimal Four Dimensional de Sitter Supergravity
• The supersymmetric solutions and extensions of ungauged matter-coupled N=1,d=4 supergravity
• Cosmological solutions from fake N=2 EYM supergravity
• Generalized instantons in N = 4 super Yang-Mills theory and spinorial geometry

Cited by in corpus (6)

• The quadric ansatz for the $mn$-dispersionless KP equation, and supersymmetric Einstein-Weyl spaces
• Einstein--Weyl Spaces and Near-Horizon Geometry
• Parallel spinors on Lorentzian Weyl spaces
• A note on the Hyper--CR equation, and gauged $N=2$ supergravity
• Recurrent Lorentzian Weyl spaces
• Killing Spinors -- Beyond Supergravity