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

Abstract

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.

72 pages, 2 figures

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Cited by in corpus (10)

• Subtracted Geometry From Harrison Transformations
• Riemannian submersions from almost contact metric manifolds
• Non-extremal Black Holes, Harmonic Functions, and Attractor Equations
• Instantons, black holes and harmonic functions
• Black holes as generalised Toda molecules
• Non-extremal black hole solutions from the c-map
• Euclidean Actions, Instantons, Solitons and Supersymmetry
• Cohomological aspects of non-Kähler manifolds
• On Non-extremal Instantons and Black Holes
• Special Geometry of Euclidean Supersymmetry IV: the local c-map