Scaling limit of the six vertex model in the framework of free field representation

The scaling limit of the spectrum, $S$ matrix, and of the form factors of the polarization operator in the six vertex model has been found. The result for the form factors is consistent with the form factors of the sine-Gordon model found recently by Lukyanov. We discuss the origin of the structure of the free field representation for the sine-Gordon model at the critical coupling from the point of view of the lattice model.Comment: 14 pages, no figures, plain TeX, all macros included, minor misprints correcte

Form factors of descendant operators: reduction to perturbed M (2, 2s + 1) models

In the framework of the algebraic approach to form factors in two-dimensional integrable models of quantum field theory we consider the reduction of the sine-Gordon model to the $\Phi_{13}$-perturbation of minimal conformal models of the $M(2,2s+1)$ series. We find in an algebraic form the condition of compatibility of local operators with the reduction. We propose a construction that make it possible to obtain reduction compatible local operators in terms of screening currents. As an application we obtain exact multiparticle form factors for the compatible with the reduction conserved currents $T_{\pm2k}$, $\Theta_{\pm(2k-2)}$, which correspond to the spin $\pm(2k-1)$ integrals of motion, for any positive integer~$k$. Furthermore, we obtain all form factors of the operators $T_{2k}T_{-2l}$, which generalize the famous $T\bar T$ operator. The construction is analytic in the $s$ parameter and, therefore, makes sense in the sine-Gordon theory.Comment: 25 pages; v2: eq. (6.2) corrected; v3: references added; v4: numerous misprints (including some reference equations) corrected; v5: annoying misprints in eqs. (1.3), (6.3) correcte