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arXiv:1405.3820 · Nuclear Physics B

Explicit boundary form factors: The scaling Lee–Yang model

László Holló, Zoltan Laczko, Zoltán Bajnok

Published Jul 23, 2014• 3 citations
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Abstract

We provide explicit expressions for boundary form factors in the boundary scaling Lee–Yang model for operators with the mildest ultraviolet behavior for all integrable boundary conditions. The form factors of the boundary stress tensor take a determinant form, while the form factors of the boundary primary field contain additional explicit polynomials.

DOI
10.1016/j.nuclphysb.2014.07.021

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We provide explicit expressions for boundary form factors in the boundary scaling Lee–Yang model for operators with the mildest ultraviolet behavior for all integrable boundary conditions. The form factors of the boundary stress tensor take a determinant form, while the form factors of the boundary primary field contain additional explicit polynomials.
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.
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.
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.
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