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 $W$ has compact critical set. 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 matrix 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 analytic models in a few classes of examples.

37 pages

References in corpus (2)

• Calabi-Yau structures on categories of matrix factorizations
• Differential models for B-type open-closed topological Landau-Ginzburg theories

Cited by in corpus (4)

• (0,2) hybrid models
• Non-degeneracy of cohomological traces for general Landau-Ginzburg models
• B-type Landau-Ginzburg models on Stein manifolds
• B-type Landau-Ginzburg models with one-dimensional target