2001/10/29 by Antoine Van Proeyen, Van Proeyen, Antoine
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0110263
21 pages, 2 figures, Contribution to the proceedings of the `Workshop on special geometric structures in string theory', Bonn, 8-11/9/2001
arxiv created 2001/10/29 · arxiv updated 2009/11/30
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.