Solitonic sectors, alpha-induction and symmetry breaking boundaries

TL;DR

This paper introduces a systematic formalism for boundary conditions that break bulk symmetries in string theory, utilizing dual fusion rings and alpha-induction, and applies it to compute physical quantities like annulus amplitudes.

Contribution

It develops a general approach to symmetry-breaking boundary conditions using dual fusion rings and alpha-induction, extending beyond the Cardy case.

Findings

Formalism for boundary conditions with broken bulk symmetries

Relation between bulk and boundary fusion rings via alpha-induction

Explicit computations of annulus amplitudes and boundary states

Abstract

We develop a systematic approach to boundary conditions that break bulk symmetries in a general way such that left and right movers are not necessarily connected by an automorphism. In the context of string compactifications, such boundary conditions typically include non-BPS branes. Our formalism is based on two dual fusion rings, one for the bulk and one for the boundary fields. Only in the Cardy case these two structures coincide. In general they are related by a version of alpha-induction. Symmetry breaking boundary conditions correspond to solitonic sectors. In examples, we compute the annulus amplitudes and boundary states.