Starting from the Bethe Ansatz solution of the open integrable spin-1 XXZ quantum spin chain with diagonal boundary terms, we derive a set of nonlinear integral equations (NLIEs), which we propose to describe the boundary supersymmetric sine-Gordon model BSSG+ with Dirichlet boundary conditions on a finite interval. We compute the corresponding boundary S matrix, and find that it coincides with the one proposed by Bajnok, Palla and Takács for the Dirichlet BSSG+ model. We derive a relation between the (UV) parameters in the boundary conditions and the (IR) parameters in the boundary S matrix. By computing the boundary vacuum energy, we determine a previously unknown parameter in the scattering theory. We solve the NLIEs numerically for intermediate values of the interval length, and find agreement with our analytical result for the effective central charge in the UV limit and with boundary conformal perturbation theory.
Bibliographical noteFunding Information:
We began this project at the APCTP Focus Program “Finite-size technology in low dimensional quantum field theory (II)” in Pohang, South Korea during summer 2005. One of us (C.A.) thanks Shizuoka University, SLAC and University of Miami for support. We are grateful to Z. Bajnok for helpful correspondence. This work was supported in part by KOSEF-M60501000025-05A0100-02500 (C.A.), by the National Science Foundation under Grants PHY-0244261 and PHY-0554821 (R.N.), and by the Ministry of Education of Japan, a Grant-in-Aid for Scientific Research 17540354 (J.S.).