Matrix factorisations for rational boundary conditions by defect fusion

TL;DR

This paper explores the realization of rational B-type boundary conditions as matrix factorisations in a specific superconformal field theory, linking Landau-Ginzburg models and rational conformal field theories through defect fusion.

Contribution

It proposes a comprehensive method to construct matrix factorisations for all rational boundary conditions in the $SU(3)/U(2)$ Kazama-Suzuki model using defect fusion techniques.

Findings

Constructed matrix factorisations for rational boundary conditions.

Linked Landau-Ginzburg models with rational conformal field theories.

Developed a functorial approach via defect fusion for matrix factorisations.

Abstract

A large class of two-dimensional $\mathcal{N}=(2,2)$ superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the $SU(3)/U(2)$ Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the $SU(3)/U(2)$ model.