### 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 φ_{id,id,adj} perturbation of the SU(2)_{k} × SU(2)_{k′}/SU(2)_{k+k′} coset models. When k′ → ∞ 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.

Original language | English |
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Pages (from-to) | 463-486 |

Number of pages | 24 |

Journal | Nuclear Physics B |

Volume | 732 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 9 2006 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Nonlinear integral equations for the finite size effects of RSOS and vertex-models and related quantum field theories.** / Hegedűs, A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Nonlinear integral equations for the finite size effects of RSOS and vertex-models and related quantum field theories

AU - Hegedűs, A.

PY - 2006/1/9

Y1 - 2006/1/9

N2 - 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 φid,id,adj perturbation of the SU(2)k × SU(2)k′/SU(2)k+k′ coset models. When k′ → ∞ 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.

AB - 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 φid,id,adj perturbation of the SU(2)k × SU(2)k′/SU(2)k+k′ coset models. When k′ → ∞ 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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U2 - 10.1016/j.nuclphysb.2005.10.041

DO - 10.1016/j.nuclphysb.2005.10.041

M3 - Article

AN - SCOPUS:28744445658

VL - 732

SP - 463

EP - 486

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -