On supersymmetric Lorentzian Einstein-Weyl spaces |
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Authors: | Patrick MeessenTomás Ortín Alberto Palomo-Lozano |
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Institution: | a HEP Theory Group, Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, E-33007 Oviedo, Spainb Instituto de Física Teórica UAM/CSIC, C/ Nicolás Cabrera 13-15, Ciudad Universitaria de Cantoblanco, E-28049 Madrid, Spain |
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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-Cività connection), or they are conformally related to certain Kundt spacetime. A full characterisation is obtained for the 4- and 6-dimensional cases. |
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Keywords: | Einstein-Weyl spaces Kundt waves Weyl geometry FakeSUGRA Supersymmetric solutions |
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