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 ${\mathbb{Z}}_2$-graded category of topological D-branes of such models.

29 pages

References in corpus (2)

• Differential models for B-type open-closed topological Landau-Ginzburg theories
• On B-type open-closed Landau-Ginzburg theories defined on Calabi-Yau Stein manifolds

Cited by in corpus (3)

• On the L2-Hodge theory of Landau-Ginzburg models
• Cohomologies of Landau-Ginzburg models
• B-type Landau-Ginzburg models with one-dimensional target