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

TL;DR

This paper explores the mathematical structure of B-branes in affine Landau-Ginzburg models, establishing a precise link between the Hochschild complex and the closed state space, and deriving correlator formulas.

Contribution

It constructs an explicit chain map linking the Hochschild complex to the closed state space and proves it is a quasi-isomorphism, providing new insights into the algebraic structure of B-branes.

Findings

Established a quasi-isomorphism between Hochschild complex and closed state space.

Derived Kapustin and Li's correlator formula from the chain map.

Provided explicit chain map construction for affine Landau-Ginzburg 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.