D-branes and matrix factorisations in supersymmetric coset models

TL;DR

This paper explores the connection between matrix factorisations and boundary states in supersymmetric coset models, identifying specific factorisations that form a basis for RR charges and can generate all boundary states.

Contribution

It establishes a correspondence between matrix factorisations and boundary states in SU(3)_k/U(2) models, expanding understanding of boundary conditions in these theories.

Findings

Identified matrix factorisations for certain boundary states.

Provided a basis for the RR charge lattice.

Suggested a method to generate all boundary states via tachyon condensation.

Abstract

Matrix factorisations describe B-type boundary conditions in N=2 supersymmetric Landau-Ginzburg models. At the infrared fixed point, they correspond to superconformal boundary states. We investigate the relation between boundary states and matrix factorisations in the Grassmannian Kazama-Suzuki coset models. For the first non-minimal series, i.e. for the models of type SU(3)_k/U(2), we identify matrix factorisations for a subset of the maximally symmetric boundary states. This set provides a basis for the RR charge lattice, and can be used to generate (presumably all) other boundary states by tachyon condensation.