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

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 ..