Finite size effects in boundary sine-Gordon theory

TL;DR

This paper investigates the boundary sine-Gordon model's spectrum and boundary energy, validating theoretical predictions with numerical methods and deriving key formulae, thus providing a comprehensive understanding of the model's boundary behavior.

Contribution

It offers a thorough validation of the boundary sine-Gordon spectrum and scattering amplitudes, including derivations of Zamolodchikov's formulae and consistency checks.

Findings

Confirmed the spectrum and reflection factors against truncated conformal space

Validated Zamolodchikov's boundary energy predictions

Provided a complete on-shell description of the boundary sine-Gordon theory

Abstract

We examine the spectrum and boundary energy in boundary sine-Gordon theory, based on our recent results on the complete spectrum predicted by closing the boundary bootstrap. We check the spectrum and the reflection factors against truncated conformal space, together with a (still unpublished) prediction by Al.B. Zamolodchikov for the boundary energy and the relation between the parameters of the scattering amplitudes and of the perturbed CFT Hamiltonian. In addition, we give a derivation of Zamolodchikov's formulae. We find an entirely consistent picture and strong evidence for the validity of the conjectured spectrum and scattering amplitudes, which together give a complete description of the boundary sine-Gordon theory on mass shell.