Defect Perturbations in Landau-Ginzburg Models

TL;DR

This paper investigates how perturbations of B-type defects in Landau-Ginzburg models affect their fusion properties and boundary conditions, revealing universal classes of perturbed defects with braid relation properties.

Contribution

It introduces a framework for analyzing defect perturbations via matrix factorizations and constructs universal perturbed defects that satisfy braid relations.

Findings

Perturbations induce boundary condition changes through defect fusion.

A universal class of perturbed defects obeys braid relations.

Fusion with these defects yields twist functors as in Seidel-Thomas theory.

Abstract

Perturbations of B-type defects in Landau-Ginzburg models are considered. In particular, the effect of perturbations of defects on their fusion is analyzed in the framework of matrix factorizations. As an application, it is discussed how fusion with perturbed defects induces perturbations on boundary conditions. It is shown that in some classes of models all boundary perturbations can be obtained in this way. Moreover, a universal class of perturbed defects is constructed, whose fusion under certain conditions obey braid relations. The functors obtained by fusing these defects with boundary conditions are twist functors as introduced in the work of Seidel and Thomas.