Permutation Branes

TL;DR

This paper develops a framework for permutation boundary states in rational conformal field theories, verifying their consistency and extending the approach to Gepner models, including the quintic Calabi-Yau.

Contribution

It introduces an ansatz for permutation boundary states, checks their consistency conditions, and applies the construction to Gepner models, providing explicit examples.

Findings

Permutation boundary states satisfy cluster and Cardy conditions.

The approach extends to Gepner models, including the quintic.

Connections between boundary and bulk OPE are explored.

Abstract

N-fold tensor products of a rational CFT carry an action of the permutation group S_N. These automorphisms can be used as gluing conditions in the study of boundary conditions for tensor product theories. We present an ansatz for such permutation boundary states and check that it satisfies the cluster condition and Cardy's constraints. For a particularly simple case, we also investigate associativity of the boundary OPE, and find an intriguing connection with the bulk OPE. In the second part of the paper, the constructions are slightly extended for application to Gepner models. We give permutation branes for the quintic, together with some formulae for their intersections.