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.
Highlights
Methods of representation theory fail in perturbed models, and analysis of local operators is more involved in this case
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 Φ13-perturbation of minimal conformal models of the M (2, 2s + 1) series
As soon as vacuum expectation values of local operators and structure constants of the operator algebra at the conformal point are known, the conformal perturbation theory can be effectively applied to analysis of primary [9] as well as descendant operators [10,11,12]
Summary
Let O(x) be a local operator, |ν1θ1, . . . , νN θN be an eigenstate (defined as an in-state) with N particles with the internal states labeled by ν1, . . . , νN and the rapidities θ1 < · · · < θN. Consider the Heisenberg algebra generated by the elements ∂a, a, d±k (k ∈ Z \ {0}) with the commutation relations [∂a, a] = 1,. The vacuum vectors define the normal ordering symbol : · · · : We assume the it will put all elements d±k with k > 0 to the right of those with k < 0. We will see that just the algebraic structure, which at the beginning seemed to be nothing but a complicated way to write down rather simple functions, makes it possible to reduce the problem to an N -independent set of equations. We construct a wide class of solutions and, among them, a set of rather useful and naturally defined local operators
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