Orbifold analysis of broken bulk symmetries

TL;DR

This paper uses orbifold techniques to analyze boundary conditions in 2D conformal field theory that break bulk symmetries, providing explicit results for abelian symmetry groups and introducing a classifying algebra.

Contribution

It introduces a new classifying algebra for symmetry-breaking boundary conditions in 2D CFT, extending the understanding of boundary symmetry structures.

Findings

Explicit results for abelian orbifold groups

Construction of a classifying algebra for boundary conditions

Relation to fusion algebra for full symmetry boundary conditions

Abstract

In two-dimensional conformal field theory, we analyze conformally invariant boundary conditions which break part of the bulk symmetries. When the subalgebra that is preserved by the boundary conditions is the fixed algebra under the action of a finite group G, orbifold techniques can be used to determine the structure of the space of such boundary conditions. We present explicit results for the case when G is abelian. In particular, we construct a classifying algebra which controls these symmetry breaking boundary conditions in the same way in which the fusion algebra governs the boundary conditions that preserve the full bulk symmetry.