Differential models for B-type open-closed topological Landau-Ginzburg theories

Abstract

We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair $(X,W)$, where $X$ is any non-compact Calabi-Yau manifold and $W$ is any holomorphic complex-valued function defined on $X$ whose critical set is compact. The models are constructed at cochain level using smooth data, including the twisted Dolbeault algebra of polyvector valued forms and a twisted Dolbeault category of holomorphic factorizations of $W$. We give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk-boundary and boundary-bulk maps of the Landau-Ginzburg theory. We prove that most of the axioms of an open-closed topological field theory are satisfied on cohomology and conjecture that the remaining axioms are also satisfied.

64 pages

References in corpus (2)

• Matrix factorisations and open topological string theory
• Calabi-Yau structures on categories of matrix factorizations

Cited by in corpus (5)

• (0,2) hybrid models
• On B-type open-closed Landau-Ginzburg theories defined on Calabi-Yau Stein manifolds
• 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