Periods for Calabi-Yau and Landau-Ginzburg vacua. (English) Zbl 0896.14022

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 many of 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 related to the mirror manifolds.


14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32G20 Period matrices, variation of Hodge structure; degenerations
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
53Z05 Applications of differential geometry to physics
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