Non-degeneracy of Cohomological Traces for General Landau-Ginzburg Models

Abstract

We prove non-degeneracy of the cohomological bulk and boundary traces for general open-closed Landau-Ginzburg models associated to a pair (X, W), where X is a non-compact complex manifold with trivial canonical line bundle and W is a complex-valued holomorphic function defined on X, assuming only that the critical locus of W is compact (but may not consist of isolated points). These results can be viewed as certain "deformed" versions of Serre duality. The first amounts to a duality property for the hypercohomology of the sheaf Koszul complex of W, while the second is equivalent with the statement that a certain power of the shift functor is a Serre functor on the even subcategory of the Z(2)-graded category of topological D-branes of such models.