Special geometries, from real to quaternionic

Details Special geometries, from real to quaternionic Special geometries, from real to quaternionic

2001-10-29

arxiv.org/abs/hep-th/0110263v1

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 2 figures, Contribution to the proceedings of the `Workshop on special geometric structures in string theory', Bonn,

Scientific paper

Special geometry is most known from 4-dimensional N=2 supergravity, though it contains also quaternionic and real geometries. In this review, we first repeat the connections between the various special geometries. Then the constructions are given starting from the superconformal approach. Without going in detail, we give the main underlying principles. We devote special attention to the quaternionic manifolds, introducing the notion of hypercomplex geometry, being manifolds close to hyperkaehler manifolds but without a metric. These are related to supersymmetry models without an action.

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