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 TFT (topological ..