International Journal of Modern Physics A

FACTORIZED CHARACTERS AND FORM FACTORS OF DESCENDANT OPERATORS IN PERTURBED CONFORMAL SYSTEMS

Philippe Christe

Published Dec 10, 1991• 29 citations

Abstract

We determine which characters of minimal models factorize into an infinite product like the one of the spin operator in the Ising model. In particular, all characters in the Ising model and in the nonunitary minimal Lee-Yang model factorize. This information is used to determine form factors of descendant operators, especially in the scaling Lee-Yang model.

DOI: 10.1142/s0217751x91002471

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International Journal of Modern Physics A

FACTORIZED CHARACTERS AND FORM FACTORS OF DESCENDANT OPERATORS IN PERTURBED CONFORMAL SYSTEMS

Philippe Christe

Published Dec 10, 1991• 29 citations

Publisher

Abstract

DOI: 10.1142/s0217751x91002471

Related papers

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Gesualdo Delfino A, Giuliano Niccoli

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.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.

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arXiv:2601.00751Jan 2, 20260 citations

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 hep-th/0407142 [1], we show numerically that the constraints on the

T\bar T

expectation values obtained by Zamolodchikov hep-th/0401146

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.

In this work, we provide a self-contained derivation of the spin-operator matrix elements in the fermionic basis, for the critical periodic Ising chain at a generic system length

N\in 2Z_{\ge 2}

. The approach relies on the near-Cauchy property of certain matrices formed by the Toeplitz symbols in the critical model, and leads to a few square-root products for the leg functions. The square root products allow simple integral representations, that further reduce to the Binet's second integral and its generalization by Hermite, in the finite volume scaling limit. This leads to product formulas for the spin operator matrix elements in the scaling limit, providing explicit expressions for the spin-operator form factors of the Ising CFT in the fermionic basis, that were computed iteratively in Yurov:1991my. They are all rational numbers up to

\sqrt{2}

. We also determine the normalization factor of the spin-operator and show explicitly how the coefficient

G(\frac{1}{2})G(\frac{3}{2})

appear through a ground state overlap. Moreover, by expanding the spin-spin two point correlator in the fermionic basis, we observed a Fredholm determinant identity that allows to show the convergence of the rescaled two-point correlator to the CFT version on a cylinder.