Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.

TL;DR

This paper thoroughly investigates boundary bound states and boundary S-matrices in the sine-Gordon model with Dirichlet boundary conditions, combining bootstrap methods and exact solutions of related integrable models.

Contribution

It introduces a comprehensive analysis of boundary bound states using bootstrap and Bethe ansatz, identifying new boundary strings and calculating boundary energies.

Findings

Identification of boundary bound states as boundary strings in Bethe ansatz

Explicit calculation of boundary energy in the sine-Gordon model

Development of boundary S-matrices using bootstrap and exact solutions

Abstract

We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution of the inhomogeneous XXZ model with boundary magnetic field and of the boundary Thirring model. We identify boundary bound states with new ``boundary strings'' in the Bethe ansatz. The boundary energy is also computed.