Flat Holomorphic Connections and Picard-Fuchs Identities From $N=2$ Supergravity

Abstract

We show that in special Kähler geometry of $N=2$ space-time supergravity the gauge variant part of the connection is holomorphic and flat (in a Riemannian sense). A set of differential identities (Picard-Fuchs identities) are satisfied on a holomorphic bundle. The relationship with the differential equations obeyed by the periods of the holomorphic three form of Calabi-Yau manifolds is outlined.

13pages

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