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Correlation functions of descendants in the scaling Lee--Yang model

Belavin, V A, Miroshnichenko, O V

Published Nov 11, 2005• 2 citations
OpenAlex

Abstract

Correlation functions of the composite field $T\\bar{T}$ in the scaling Lee--Yang model are studied. Using the analytic expression for form factors of this operator recently proposed by Delfino and Niccoli \\cite{DN}, we show numerically that the constraints on the $T\\bar{T}$ expectation values obtained in \\cite{AZ_VEVTT} and the additional requirement of asymptotic behavior lead to a perfect agreement with the ultraviolet asymptotic predicted by the conformal perturbation theory.

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Correlation functions of the composite field TbarTT\\bar{T}TbarT in the scaling Lee--Yang model are studied. Using the analytic expression for form factors of this operator recently proposed by Delfino and Niccoli \cite{DN}, we show numerically that the constraints on the TbarTT\\bar{T}TbarT expectation values obtained in \cite{AZ_VEVTT} and the additional requirement of asymptotic behavior lead to a perfect agreement with the ultraviolet asymptotic predicted by the conformal perturbation theory.
Correlation functions of the composite field TTˉT\bar TTTˉ in the scaling Lee-Yang model are studied. Using the analytic expression for form factors of this operator recently proposed by Delfino and Niccoli hep-th/0407142 [1], we show numerically that the constraints on the TTˉT\bar TTTˉ expectation values obtained by Zamolodchikov hep-th/0401146
The form factors of the descendant operators in the massive Lee–Yang model are determined up to level 7. This is first done by exploiting the conserved quantities of the integrable theory to generate the solutions for the descendants starting from the lowest non-trivial solutions in each operator family. We then show that the operator space generated in this way, which is isomorphic to the conformal one, coincides, level by level, with that implied by the S -matrix through the form factor bootstrap. The solutions that we determine satisfy asymptotic conditions carrying the information about the level that we conjecture to hold for all the operators of the model.
We consider the scaling Lee - Yang model. It corresponds to the unique perturbation of the minimal CFT model . This model is not unitary. We are using an expression for form factors in terms of symmetric polynomials in order to obtain a closed expression for the correlation function of the trace of the energy-momentum tensor. This expression is a determinant of an integral operator. Similar determinant representations were proven to be useful not only for quantum correlation functions but also in matrix models.
We consider the one-point functions of bulk and boundary fields in the scaling Lee-Yang model for various combinations of bulk and boundary perturbations. The one-point functions of the bulk fields are analysed using the truncated conformal space approach and the form-factor expansion. Good agreement is found between the results of the two methods, though we find that the expression for the general boundary state given by Ghoshal and Zamolodchikov has to be corrected slightly. For the boundary fields we use thermodynamic Bethe ansatz equations to find exact expressions for the strip and semi-infinite cylinder geometries. We also find a novel off-critical identity between the cylinder partition functions of models with differing boundary conditions, and use this to investigate the regions of boundary-induced instability exhibited by the model on a finite strip.