Permutation branes and linear matrix factorisations

TL;DR

This paper establishes a correspondence between permutation branes in Gepner models and matrix factorisations of Landau-Ginzburg potentials, advancing the understanding of topological branes in string theory.

Contribution

It identifies the matrix factorisations associated with arbitrary B-type permutation branes in Gepner models, providing a new algebraic description.

Findings

Permutation branes can be encoded as matrix factorisations.

The paper generalizes the correspondence to arbitrary B-type permutation branes.

Enhances the algebraic understanding of topological branes in string theory.

Abstract

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.