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

TL;DR

This paper develops an algebraic approach to form factors in integrable quantum field theories, specifically reducing the sine-Gordon model to minimal conformal models, and constructs exact form factors for conserved currents and operators related to the $Tar T$ deformation.

Contribution

It introduces a method to obtain reduction-compatible local operators and exact form factors for conserved currents and operators in the reduced models.

Findings

Derived algebraic conditions for operator compatibility with reduction.

Constructed exact multiparticle form factors for conserved currents.

Obtained form factors for operators generalizing the $Tar T$ operator.

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 $T_{\pm2k}$, $\Theta_{\pm(2k-2)}$, 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.