The closed state space of affine Landau–Ginzburg B-models

Abstract

We study the category of perfect cdg-modules over a curved algebra, and in particular the category of B-branes in an affine Landau–Ginzburg model. We construct an explicit chain map from the Hochschild complex of the category to the closed state space of the model, and prove that this is a quasi-isomorphism from the Borel–Moore Hochschild complex. Using the lowest-order term of our map we derive Kapustin and Li’s formula for the correlator of an open-string state over a disc.