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On B-type Open–Closed Landau–Ginzburg Theories Defined on Calabi–Yau Stein Manifolds

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Abstract

We consider the bulk algebra and topological D-brane category arising from the differential model of the open–closed B-type topological Landau–Ginzburg theory defined by a pair (X,W), where X is a non-compact Calabi–Yau manifold and W is a complex-valued holomorphic function. When X is a Stein manifold (but not restricted to be a domain of holomorphy), we extract equivalent descriptions of the bulk algebra and of the category of topological D-branes which are constructed using only the analytic space associated to X. In particular, we show that the D-brane category is described by projective factorizations defined over the ring of holomorphic functions of X. We also discuss simplifications of the analytic models which arise when X is holomorphically parallelizable and illustrate these in a few classes of examples.

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Correspondence to Elena Mirela Babalic.

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Babalic, E.M., Doryn, D., Lazaroiu, C.I. et al. On B-type Open–Closed Landau–Ginzburg Theories Defined on Calabi–Yau Stein Manifolds. Commun. Math. Phys. 362, 129–165 (2018). https://doi.org/10.1007/s00220-018-3153-5

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