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.
Cite
@article{arxiv.1107.0937,
title = {On supersymmetric Einstein-Weyl spaces},
author = {P. Meessen and T. Ortín and A. Palomo-Lozano},
journal= {arXiv preprint arXiv:1107.0937},
year = {2011}
}
Comments
17 pages, version to be published in JGP