NLIE of Dirichlet sine-Gordon Model for Boundary Bound States

TL;DR

This paper derives a nonlinear integral equation for boundary excited states in the sine-Gordon model with Dirichlet boundaries, connecting IR scattering data with UV conformal field theory, and compares boundary energies and reflection factors.

Contribution

It introduces a new NLIE for boundary excited states derived from Bethe ansatz, linking IR and UV data in the boundary sine-Gordon model.

Findings

Calculated boundary energies and reflection factors

Established correspondence between IR scattering and UV conformal data

Compared boundary states with previous theoretical predictions

Abstract

We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Luscher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory.