Boundary breathers in the sinh-Gordon model

TL;DR

This paper investigates boundary breather states in the sinh-Gordon model on a half-line, deriving the energy spectrum through bootstrap and WKB methods, and establishing relationships between boundary parameters, bulk coupling, and reflection factors.

Contribution

It provides a detailed analysis of boundary breather states in the sinh-Gordon model, combining classical solutions with quantum spectrum calculations to relate boundary parameters and scattering data.

Findings

Classical boundary breather solutions for a two-parameter family of boundary conditions.

Quantum energy spectrum computed via bootstrap and WKB methods.

Consistency between methods determines relationships among boundary parameters, bulk coupling, and reflection factors.

Abstract

We present an investigation of the boundary breather states of the sinh-Gordon model restricted to a half-line. The classical boundary breathers are presented for a two parameter family of integrable boundary conditions. Restricting to the case of boundary conditions which preserve the \phi --> -\phi symmetry of the bulk theory, the energy spectrum of the boundary states is computed in two ways: firstly, by using the bootstrap technique and subsequently, by using a WKB approximation. Requiring that the two descriptions of the spectrum agree with each other allows a determination of the relationship between the boundary parameter, the bulk coupling constant, and the parameter appearing in the reflection factor derived by Ghoshal to describe the scattering of the sinh-Gordon particle from the boundary.