Free-Field Representation of Permutation Branes in Gepner Models

TL;DR

This paper develops a free-field approach to construct permutation branes in Gepner models, identifying boundary conditions compatible with minimal model structures.

Contribution

It introduces a novel free-field realization method for permutation branes in Gepner models, providing explicit constructions.

Findings

Permutation boundary conditions are characterized by permutation matrices.

The approach ensures compatibility with the singular vectors structure of minimal models.

Explicit free-field constructions of permutation branes are achieved.

Abstract

We consider free-field realization of Gepner models basing on free-field realization of N=2 superconformal minimal models. Using this realization we analyse A/B-type boundary conditions starting from the ansatz when left-moving and right-moving free-fields degrees of freedom are glued at the boundary by an arbitrary constant matrix. It is shown that the only boundary conditions consistent with the singular vectors structure of unitary minimal models representations are given by permutation matrices and give thereby explicit free-field construction of permutation branes of Recknagel.