Considerations of One-Modulus Calabi-Yau Compactifications: Picard-Fuchs Equations, Kähler Potentials and Mirror Maps

Abstract

We consider Calabi-Yau compactifications with one Kähler modulus. Following the method of Candelas et al. we use the mirror hypothesis to solve the quantum theory exactly in dependence of this modulus by performing the calculation for the corresponding complex structure deformation on the mirror manifold. Here the information is accessible by techniques of classical geometry. It is encoded in the Picard-Fuchs differential equation which has to be supplemented by requirements on the global properties of its solutions.

25 pages (+ 6 figures not included, available in postscript)

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• Duality Anomaly Cancellation, Minimal String Unification and the Effective Low-Energy Lagrangian of 4-D Strings
• Topological Field Theory and Rational Curves
• Picard-Fuchs equations and mirror maps for hypersurfaces
• Periods and Duality Symmetries in Calabi-Yau Compactifications
• Picard-Fuchs Equations and Special Geometry
• Flat Holomorphic Connections and Picard-Fuchs Identities From $N=2$ Supergravity

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