B-type defects in Landau-Ginzburg models

TL;DR

This paper develops a comprehensive LG-based framework for B-type defects in N=(2,2) theories, formulating defects as matrix factorisations of W1−W2 and detailing their fusion and action on B-type boundaries. It demonstrates that defect composition is captured by tensor products of matrix factorisations and shows how to reduce infinite-rank tensor products to finite-rank, physically meaningful boundary conditions. The authors analyze explicit LG examples W=X^d and W=X^d+Z^2, deriving fusion rules for permutation-type and symmetry defects, and they rigorously compare these LG results with the corresponding CFT descriptions of defects in N=2 minimal models, finding complete agreement. The work also clarifies the role of symmetry defects, Knörrer periodicity, and the folding trick in connecting LG defects to IR CFT data, with implications for the geometric understanding of D-branes via Fourier–Mukai transforms.

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.