Symmetry Breaking Boundary States and Defect Lines

TL;DR

The paper develops a general algebraic framework for symmetry-breaking boundary states in coset CFTs, extending the GKO construction to non-abelian denominators. By decomposing the bulk Hilbert space under the smaller chiral algebra $ ext{A}( ext{G}/ ext{P})igoplus ext{A}( ext{P})$ and solving appropriate Cardy-type constraints, it yields explicit boundary states with computable open-string spectra, even when the preserved symmetry is smaller than the bulk. The authors connect their cosine-based states to orbifold constructions, provide concrete examples (including Ising-like cases), and show how the same machinery yields non-factorizing boundary conditions in product geometries and defect lines between CFTs with jumping central charge. The results have potential implications for D-branes in curved backgrounds and AdS/CFT, as well as for understanding Casimir energies and defect-induced transport across interfaces. The work also outlines directions for extending the method, resolving fixed points, and obtaining boundary OPE data via sewing constraints.

Abstract

We present a large and universal class of new boundary states which break part of the chiral symmetry in the underlying bulk theory. Our formulas are based on coset constructions and they can be regarded as a non-abelian generalization of the ideas that were used by Maldacena, Moore and Seiberg to build new boundary states for SU(N). We apply our expressions to construct defect lines joining two conformal field theories with possibly different central charge. Such defects can occur e.g. in the AdS/CFT correspondence when branes extend to the boundary of the AdS-space.

Figures (1)

• Figure 1: The folding trick relates a system on the real line with a defect to a tensor product theory on the half line.