Nonlinear integral equations for the finite size effects of RSOS and vertex-models and related quantum field theories

Abstract

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 ${\varphi }_{id,id,adj}$ perturbation of the $SU(2{)}_k\times SU(2{)}_{k^{\prime }}/SU(2{)}_{k+k^{\prime }}$ coset models. When $k^{\prime }\to \infty$ 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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Cited by in corpus (10)

• Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics
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• Finite Size Spectrum of SU(N) Principal Chiral Field from Discrete Hirota Dynamics
• Exact finite size spectrum in super sine-Gordon model
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
• Finite size effects and 2-string deviations in the spin-1 XXZ chains
• Contour deformation trick in hybrid NLIE
• Scattering matrix for a general gl(2) spin chain
• On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model