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Periods for Calabi-Yau and Landau-Ginzburg vacua. (English) Zbl 1009.32500
Summary: The complete structure of the moduli space of Calabi-Yau manifolds and the associated Landau-Ginzburg theories, and hence also of the corresponding low-energy effective theory that results from $(2, 2)$ superstring compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calculable for a great many such models. We illustrate this by computing the periods explicitly for a number of classes of Calabi-Yau manifolds. We also point out that it is possible to read off from the periods certain important information relating to the mirror manifolds.

32G20Period matrices, variation of Hodge structure; degenerations
14J32Calabi-Yau manifolds
32G81Applications of deformations of analytic structures to physics
32J81Applications of compact analytic spaces to physics
81T40Two-dimensional field theories, conformal field theories, etc.
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