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New developments in special geometry

Abstract

We review recent developments in special geometry, emphasizing the role of real coordinates. In the first part we discuss the para-complex geometry of vector and hypermultiplets in rigid Euclidean N=2 supersymmetry. In the second part we study the variational principle governing the near horizon limit of BPS black holes in matter-coupled N=2 supergravity and observe that the black hole entropy is the Legendre transform of the Hesse potential encoding the geometry of the scalar fields.Comment: 27 pages, contributed to the Handbook on Pseudo-Riemannian Geometry and Supersymmetr

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