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

Abstract

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 $T_{\pm 2k}$, ${\Theta }_{\pm (2k-2)}$, 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.

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) corrected

References in corpus (7)

• Hidden Grassmann structure in the XXZ model
• Fermionic structure in the sine-Gordon model: form factors and null-vectors
• The composite operator T\bar{T} in sinh-Gordon and a series of massive minimal models
• Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory
• Form factors in sinh- and sine-Gordon models, deformed Virasoro algebra, Macdonald polynomials and resonance identities
• On form factors and Macdonald polynomials
• Form factors of descendant operators: Resonance identities in the sinh-Gordon model

Cited by in corpus (3)

• The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations
• Lattice models, deformed Virasoro algebra and reduction equation
• Note on four-particle form factors of operators $T_{2n}{T}_{-2n}$ in sinh-Gordon model