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 Lüscher 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.
Bibliographical noteFunding Information:
The authors would like to thank R. Nepomechie and G. Takács for the illuminating discussions and for taking part in the early stages of this work. This research was partially supported by the Hungarian research funds OTKA K60040 and by a cooperation between the Hungarian Academy of Sciences and the Korean KOSEF. C.A. was supported in part by a Korea Research Foundation Grant funded by the Korean government (MOEHRD) (KRF-2006-312-C00096) and Z.B. was supported by a Bolyai Scholarship and the EC network “Superstring”. F.R. thanks partial financial support from the INFN Grant TO12, from the Italian Ministry of University and Research through a PRIN fund and from the NATO Collaborative Linkage Grant PST.CLG.980424.
- Boundary sine-Gordon theory
- XXZ spin chain