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Picard-Fuchs Equations and Special Geometry

A. Ceresole·R. D'Auria·S. Ferrara·W. Lerche·J. Louis
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Abstract

We investigate the system of holomorphic differential identities implied by special Kählerian geometry of four-dimensional N=2 supergravity. For superstring compactifications on \cy threefolds these identities are equivalent to the Picard-Fuchs equations of algebraic geometry that are obeyed by the periods of the holomorphic three-form. For one variable they reduce to linear fourth-order equations which are characterized by classical $W$-generators; we find that the instanton corrections to the Yukawa couplings are directly related to the non-vanishing of $w_4$. We also show that the symplectic structure of special geometry can be related to the fact that the Yukawa couplings can be written as triple derivatives of some holomorphic function $F$. Moreover, we give the precise relationship of the Yukawa couplings of special geometry with three-point functions in topological field theory.

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A. Ceresole, R. D'Auria, S. Ferrara, W. Lerche, J. Louis. 1992-04-15. Picard-Fuchs Equations and Special Geometry. https://doi.org/10.1142/s0217751x93000047

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