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

The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations

We study quasilocal operators in the quantum complex sinh-Gordon theory in the form factor approach. The free field procedure for descendant operators is developed by introducing the algebra of screening currents and related algebraic objects. We work out null vector equations in the space of operators. Further we apply the proposed algebraic structures to constructing form factors of the conserved currents $T_k$ and $\Theta_k$. We propose also form factors of current-current operators of the form $T_kT_{-l}$. Explicit computations of the four-particle form factors allow us to verify the recent conjecture of Smirnov and Zamolodchikov about the structure of the exact scattering matrix of an integrable theory perturbed by a combination of irrelevant operators. Our calculations confirm that such perturbations of the complex sinh-Gordon model and of the $\mathbb Z_N$ symmetric Ising models result in extra CDD factors in the $S$ matrix.Comment: 31 pages; v2: references added; v3: many misprints correcte

Lukyanov's Screening Operators for the Deformed Virasoro Algebra

The BRST property of Lukyanov's screening operators in the bosonic representation of the deformed Virasoro algebra is proven.Comment: Minor misprints correcte

Multi-point Local Height Probabilities in the Integrable RSOS Model

By using the bosonization technique, we derive an integral representation for multi-point Local Hight Probabilities for the Andrews-Baxter-Forrester model in the regime III. We argue that the dynamical symmetry of the model is provided by the deformed Virasoro algebra.Comment: 29 pages, harvmac.tex, 12 eps figures, epsf.tex, revised version, corrections in subsection 4.2, the main results are unchange