On supersymmetric Einstein-Weyl spaces

Details On supersymmetric Einstein-Weyl spaces On supersymmetric Einstein-Weyl spaces

2011-07-05

arxiv.org/abs/1107.0937v3

J. Geom. Phys. 62(2012), 301

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, version to be published in JGP

Scientific paper

10.1016/j.geomphys.2011.10.017

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.

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