Five Dimensional Minimal Supergravities and Four Dimensional Complex Geometries

Details Five Dimensional Minimal Supergravities and Four Dimensional Complex Geometries Five Dimensional Minimal Supergravities and Four Dimensional Complex Geometries

2009-01-26

arxiv.org/abs/0901.4066v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages. Contribution to the Proceedings of the Spanish Relativity Meeting 2008 in Salamanca, Spain

Scientific paper

We discuss the relation between solutions admitting Killing spinors of minimal supergravities in five dimensions and four dimensional complex geometries. In the ungauged case (vanishing cosmological constant \Lambda=0) the solutions are determined in terms of a hyper-Kahler base space; in the gauged case (\Lambda<0) the complex geometry is Kahler; in the de Sitter case (\Lambda>0) the complex geometry is hyper-Kahler with torsion (HKT). In the latter case some details of the derivation are given. The method for constructing explicit solutions is discussed in each case.

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