Developments in special geometry

Details Developments in special geometry Developments in special geometry

2011-12-13

arxiv.org/abs/1112.2873v2

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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.

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