Hidden symmetries, special geometry and quaternionic manifolds

Details Hidden symmetries, special geometry and quaternionic manifolds Hidden symmetries, special geometry and quaternionic manifolds

1993-10-13

arxiv.org/abs/hep-th/9310067v1

Int.J.Mod.Phys.D3:31-48,1994

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1142/S0218271894000058

The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in $N=2$ supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces are implemented via dimensional reduction. We analyze the emergence of {\em extra} and {\em hidden} symmetries. This analysis is then applied to homogeneous special spaces and the implications for the classification of homogeneous quaternionic spaces are discussed.

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