Landau-Ginzburg Realization of Open String TFT

TL;DR

This paper explores B-type topological Landau-Ginzburg theory with boundary conditions, analyzing brane configurations, computing open string rings, and establishing its equivalence to a mathematical category, thus confirming its internal consistency.

Contribution

It provides a detailed analysis of D2-brane boundary conditions, computes open string chiral rings, and links the physical model to Kontsevich's triangulated category, offering a concrete realization.

Findings

Brane configurations determined by superpotential factorizations

Open string rings characterized by generators and relations

Disk correlators satisfy topological sewing constraints

Abstract

We investigate B-type topological Landau-Ginzburg theory with one variable, with D2-brane boundary conditions. We find that the allowed brane configurations are determined in terms of the possible factorizations of the superpotential, and compute the corresponding open string chiral rings. These are characterized by bosonic and fermionic generators that satisfy certain relations. Moreover we show that the disk correlators, being continuous functions of deformation parameters, satisfy the topological sewing constraints, thereby proving consistency of the theory. In addition we show that the open string LG model is, in its content, equivalent to a certain triangulated category introduced by Kontsevich, and thus may be viewed as a concrete physical realization of it.