Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes

Details Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes

2009-05-18

arxiv.org/abs/0905.2844v1

JHEP 0907:066,2009

Physics

High Energy Physics

High Energy Physics - Theory

72 pages, 2 figures

Scientific paper

10.1088/1126-6708/2009/07/066

We define and study projective special para-Kahler manifolds and show that they appear as target manifolds when reducing five-dimensional vector multiplets coupled to supergravity with respect to time. The dimensional reductions with respect to time and space are carried out in a uniform way using an epsilon-complex notation. We explain the relation of our formalism to other formalisms of special geometry used in the literature. In the second part of the paper we investigate instanton solutions and their dimensional lifting to black holes. We show that the instanton action, which can be defined after dualising axions into tensor fields, agrees with the ADM mass of the corresponding black hole. The relation between actions via Wick rotation, Hodge dualisation and analytic continuation of axions is discussed.

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