Picard-Fuchs Equations and Special Geometry

Details Picard-Fuchs Equations and Special Geometry Picard-Fuchs Equations and Special Geometry

1992-04-15

arxiv.org/abs/hep-th/9204035v1

Int.J.Mod.Phys. A8 (1993) 79-114

Physics

High Energy Physics

High Energy Physics - Theory

43 pages

Scientific paper

We investigate the system of holomorphic differential identities implied by special K\"ahlerian 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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