A ug 2 00 1 THE SPECTRUM OF BOUNDARY SINE - GORDON THEORY ∗

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the spectrum of boundary states by closing the boundary bootstrap and gave a derivation of Al.B. Zamolodchikov's (unpublished) formulae for the boundary energy and the relation between the Lagrangian (ultraviolet) and bootstrap (infrared) parameters.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 con-formal 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. 1. Introduction In these proceedings we report on the results of our works [1, 2, 3]. Instead of following the line of the original conference talk, we wish to give a summary of the results and conjectures which together describe the on-shell spectral data of boundary sine-Gordon theory. Sine-Gordon field theory is one of the most important quantum field theoretic models with numerous applications ranging from particle the-oretic problems to condensed matter systems, and one which has played a central role in our understanding of 1 + 1 dimensional field theories. A crucial property of the model is integrability, which permits an exact analytic determination of many of its physical properties and characteristic quantities. Integrability can also be preserved in the presence of bound-* Original title of the conference talk: Sine-Gordon with Neumann boundary condition: the spectrum of boundary states † Conference speaker