Boundary bound states in integrable quantum field theories

TL;DR

This paper discusses recent progress in calculating non-perturbative reflection factors for the sinh-Gordon model with integrable boundary conditions, using boundary bootstrap and classical solution quantization methods.

Contribution

It introduces a novel approach to determine boundary reflection factors by comparing bootstrap and classical quantization in integrable quantum field theories.

Findings

Derived boundary reflection factors for sinh-Gordon model.

Validated reflection factors through two independent methods.

Enhanced understanding of boundary effects in integrable models.

Abstract

The purpose of this talk is to sketch some recent progress which has been made in calculating non-perturbatively the reflection factors for the sinh-Gordon model restricted to a half-line by integrable boundary conditions. The essential idea is to calculate the energy spectrum of boundary breathers in two independent ways; firstly by using the boundary bootstrap and secondly by quantizing the classical solutions corresponding to boundary breathers. Comparing these two calculations provides a way to determine the dependence of the reflection factors on the parameters introduced into the Lagrangian by the boundary conditions. The basic idea is illustrated using a massive free scalar field with a linear boundary condition confining it to a half-line.