Nonlinear Integral Equation and Finite Volume Spectrum of Sine-Gordon Theory

Abstract

We examine the connection between the nonlinear integral equation (NLIE) derived from light-cone lattice and sine-Gordon quantum field theory, considered as a perturbed c=1 conformal field theory. After clarifying some delicate points of the NLIE deduction from the lattice, we compare both analytic and numerical predictions of the NLIE to previously known results in sine-Gordon theory. To provide the basis for the numerical comparison we use data from Truncated Conformal Space method. Together with results from analysis of infrared and ultraviolet asymptotics, we find evidence that it is necessary to change the rule of quantization proposed by Destri and de Vega to a new one which includes as a special case that of Fioravanti et al. This way we find strong evidence for the validity of the NLIE as a description of the finite size effects of sine-Gordon theory.

LaTeX2e, 49 pages, 14 eps figures. Presentation shortened and improved, some typos corrected

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• Non linear integral equation and excited--states scaling functions in the sine-Gordon model
• Truncated Conformal Space at c=1, Nonlinear Integral Equation and Quantization Rules for Multi-Soliton States
• Excited states in some simple perturbed conformal field theories
• Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras

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