Special Kähler geometry. An intrinsic formulation from N=2 space-time supersymmetry

Abstract

N=2, 4D supergravity coupled to vector multiplets (1, 12, 0) is reanalysed in a geometrical setting. By requiring the closure of the supersymmetry transformation laws, we find a coordinate-free characterization of the manifold M spanned by the scalar fields. The geometry of M, called “special geometry”, is relevant to compactified string theories, since it is common to the moduli spaces of Calabi-Yau threefolds and c=9 (2, 2) superconformal field theories.