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

TL;DR

This paper explores the geometry of Euclidean supersymmetry, focusing on projective special para-Kahler manifolds, and investigates instanton solutions and their relation to black holes through dimensional reduction and dualities.

Contribution

It introduces the formalism of projective special para-Kahler manifolds in the context of Euclidean supersymmetry and relates instanton actions to black hole masses.

Findings

Defined and studied projective special para-Kahler manifolds.

Established the relation between instanton actions and black hole masses.

Unified dimensional reduction formalism using epsilon-complex notation.

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.