Special geometry and symplectic transformations

Special Kähler manifolds are defined by coupling of vector multiplets to N = 2 supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain n vectors in rigid supersymmetry and n + 1 in supergravity, and n complex scalars. Apart from exceptional cases they are de...

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Published in:Nuclear physics. Section B, Proceedings supplement Proceedings supplement, 1996-02, Vol.45 (2), p.196-206
Main Authors: de Wit, Bernard, Van Proeyen, Antoine
Format: Article
Language:English
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Summary:Special Kähler manifolds are defined by coupling of vector multiplets to N = 2 supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain n vectors in rigid supersymmetry and n + 1 in supergravity, and n complex scalars. Apart from exceptional cases they are defined by a holomorphic function of the scalars. For supergravity this function is homogeneous of second degree in an ( n + 1)-dimensional projective space. Another formulation exists which does not start from this function, but from a symplectic (2 n)-or (2 n + 2)-dimensional complex space. Symplectic transformations lead either to isometries on the manifold or to symplectic reparametrizations. Finally we touch on the connection with special quaternionic and very special real manifolds, and the classification of homogeneous special manifolds.
ISSN:0920-5632
1873-3832
DOI:10.1016/0920-5632(95)00637-0