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Matrix factorizations for nonaffine LG-models. (English) Zbl 1243.81178

Summary: We propose a natural definition of a category of matrix factorizations for nonaffine Landau-Ginzburg models. For any LG-model we construct a fully faithful functor from the category of matrix factorizations defined in this way to the triangulated category of singularities of the corresponding fiber. We also show that this functor is an equivalence if the total space of the LG-model is smooth.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
18E30 Derived categories, triangulated categories (MSC2010)
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