Boundary spectrum in the sine-Gordon model with Dirichlet boundary conditions

TL;DR

This paper determines the boundary bound state spectrum in the sine-Gordon model with Dirichlet conditions, completing the bootstrap and analyzing boundary reflection poles using a novel boundary Coleman-Thun mechanism.

Contribution

It introduces a complete boundary spectrum analysis for the sine-Gordon model and proposes two general lemmas applicable to any 1+1-dimensional boundary field theory.

Findings

Complete boundary bound state spectrum identified

Boundary reflection poles fully characterized

Boundary Coleman-Thun mechanism elucidated

Abstract

We find the spectrum of boundary bound states for the sine-Gordon model with Dirichlet boundary conditions, closing the bootstrap and providing a complete description of all the poles in the boundary reflection factors. The boundary Coleman-Thun mechanism plays an important role in the analysis. Two basic lemmas are introduced which should hold for any 1+1-dimensional boundary field theory, allowing the general method to be applied to other models.