A differential model for B-Type Landau–Ginzburg theories

Abstract

We describe a mathematically rigorous differential model for B-Type open-closed topological Landau–Ginzburg theories defined by a pair (X,W), where X is a non-compact Kählerian manifold with holomorphically trivial canonical line bundle andW is a complex-valued holomorphic function defined on X and whose critical locus is compact but need not consist of isolated points. We also show how this construction specializes to the case when X is Stein and W has finite critical set, in which case one recovers a simpler mathematical model.