Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-07-14
Nucl.Phys. B732 (2005) 463-486
Physics
High Energy Physics
High Energy Physics - Theory
Scientific paper
10.1016/j.nuclphysb.2005.10.041
Starting from critical RSOS lattice models with appropriate inhomogeneities, we derive two component nonlinear integral equations to describe the finite volume ground state energy of the massive $\phi_{id,id,adj}$ perturbation of the $SU(2)_k \times SU(2)_{k'} /SU(2)_{k+k'}$ coset models. When $k' \to \infty$ while the value of $k$ is fixed, the equations correspond to the current-current perturbation of the $SU(2)_k$ WZW model. Then modifying one of the kernel functions of these equations, we propose two component nonlinear integral equations for the fractional supersymmetric sine-Gordon models. The lattice versions of our equations describe the finite size effects in the corresponding lattice models, namely in the critical RSOS($k,q$) models, in the isotropic higher-spin vertex models, and in the anisotropic higher-spin vertex models. Numerical and analytical checks are also performed to confirm the correctness of our equations. These type of equations make it easier to treat the excited state problem.
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