Symmetry-breaking boundary states for WZW models

TL;DR

This paper constructs novel boundary states in SU(2)_k WZW models that break some symmetries, revealing new classes of boundary conditions and their extensions to other models.

Contribution

It introduces a method to build symmetry-breaking boundary states in WZW models, including special cases related to discrete quotients and embeddings into higher groups.

Findings

Boundary states preserve parafermion and Virasoro subalgebras.

Families of boundary states depend on the level k and group quotients.

New boundary states can be extended to other WZW models via embeddings.

Abstract

Starting with the SU(2)_k WZW model, we construct boundary states that generically preserve only a parafermion times Virasoro subalgebra of the full affine Lie algebra symmetry of the bulk model. The boundary states come in families: intervals for generic k, quotients of SU(2) by discrete groups if k is a square. In that case, special members of the families can be viewed as superpositions of rotated Cardy branes. Using embeddings of SU(2) into higher groups, the new boundary states can be lifted to symmetry-breaking branes for other WZW models.