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arXiv · hep-th/9612239

Mirror Symmetry and the Web of Landau-Ginzburg String Vacua

Hitoshi Sato
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Abstract

We present some mathematical aspects of Landau-Ginzburg string vacua in terms of toric geometry. The one-to-one correspondence between toric divisors and some of (-1,1) states in Landau-Ginzburg model is presented for superpotentials of typical types. The Landau-Ginzburg interpretation of non-toric divisors is also presented. Using this interpretation, we propose a method to solve the so-called "twisted sector problem" by orbifold construction. Moreover,this construction shows that the moduli spaces of the original Landau-Ginzburg string vacua and their orbifolds are connected. By considering the mirror map of Landau-Ginzburg models, we obtain the relation between Mori vectors and the twist operators of our orbifoldization. This consideration enables us to argue the embedding of the Seiberg-Witten curve in the defining equation of the Calabi-Yau manifoulds on which the type II string gets compactified. Related topics concerning the Calabi-Yau fourfolds and the extremal transition are discussed.

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Hitoshi Sato. 1997-05-15. Mirror Symmetry and the Web of Landau-Ginzburg String Vacua. https://doi.org/10.1016/s0550-3213(97)00471-9

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