Developments in special geometry

Abstract

We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we disucss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

Submitted to the proceedings of QTS 7, Prague, August 2011. Revised version: references added

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Cited by in corpus (5)

• Nonextremal black holes in gauged supergravity and the real formulation of special geometry
• The Hesse potential, the c-map and black hole solutions
• Special Geometry, Hessian Structures and Applications
• Non-holomorphic deformations of special geometry and their applications
• Non-extremal black holes from the generalised r-map