The spectrum of boundary sine-Gordon theory

TL;DR

This paper reviews the on-shell spectrum and boundary states of the integrable boundary sine-Gordon model, confirming conjectured formulas through numerical checks and providing a complete mass-shell description.

Contribution

It derives boundary state spectra, confirms Zamolodchikov's formulas, and links Lagrangian and bootstrap parameters in boundary sine-Gordon theory.

Findings

Confirmed boundary state spectrum via boundary bootstrap.

Validated Zamolodchikov's boundary energy formulas.

Supported the complete on-shell description with numerical evidence.

Abstract

We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states by closing the boundary bootstrap and gave a derivation of Al.B. Zamolodchikov's (unpublished) formulae for the boundary energy and the relation between the Lagrangian (ultraviolet) and bootstrap (infrared) parameters. These results have been checked against numerical finite volume spectra coming from the truncated conformal space approach. 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.