On B-type open-closed Landau-Ginzburg theories defined on Calabi-Yau Stein manifolds. (English) Zbl 1397.32008
Summary: 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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