Symmetry breaking boundaries I. General theory

TL;DR

This paper develops a comprehensive theoretical framework for conformally invariant boundary conditions that break bulk symmetries, including explicit constructions and proofs of key properties.

Contribution

It introduces a general theory for boundary conditions with fixed subalgebras under abelian orbifold groups, including explicit boundary state and amplitude constructions.

Findings

Constructed boundary states and reflection coefficients

Proved integrality of annulus coefficients

Provided a general theoretical framework

Abstract

We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group. We explicitly construct the boundary states and reflection coefficients as well as the annulus amplitudes. Integrality of the annulus coefficients is proven in full generality.