Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-10-25
Nucl.Phys.Proc.Suppl. 45BC (1996) 196-206
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, latex using espcrc2, no figures. Some factors and minor corrections. Version to be published in the proceedings of t
Scientific paper
10.1016/0920-5632(95)00637-0
Special Kahler 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 $(2n)$- or $(2n+2)$-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.
Proeyen Antoine Van
Wit Bernard de
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