B-type defects in Landau-Ginzburg models

TL;DR

This paper studies B-type defects in Landau-Ginzburg models using matrix factorizations, analyzing their composition and action on boundary conditions, and compares results with conformal field theory in specific models.

Contribution

It introduces a matrix factorization framework for B-type defects in Landau-Ginzburg models and compares these with conformal field theory results.

Findings

Matrix factorizations represent B-type defects.

Defect composition and boundary actions are explicitly described.

Comparison with CFT confirms the Landau-Ginzburg approach.

Abstract

We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the superpotentials. The composition of these defects and their action on B-type boundary conditions is described in this framework. The cases of Landau-Ginzburg models with superpotential W=X^d and W=X^d+Z^2 are analysed in detail, and the results are compared to the CFT treatment of defects in N=2 superconformal minimal models to which these Landau-Ginzburg models flow in the IR.