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Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation

Mathias Pillin

Published Jan 1, 1999• 2 citations
OpenAlex

Abstract

Dedicated to the memory of Moshé Flato The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (“replica”) deformation of the form factor approach. We show that replicadeformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational sl2-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether The form factor approach to massive integrable quantum field theories (QFTs) [9, 20] provides a powerful tool to compute exact matrix elements of local operators from the knowledge of the (factorized) S-matrix. To be precise, a form factor in this context is the matrix element of some local operator between the physical vacuum and a multi-particle

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•Jan 1, 2003•5 citations
Dedicated to the memory of Moshé Flato The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (“replica”) deformation of the form factor approach. We show that replicadeformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational sl2-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether The form factor approach to massive integrable quantum field theories (QFTs) [9, 20] provides a powerful tool to compute exact matrix elements of local operators from the knowledge of the (factorized) S-matrix. To be precise, a form factor in this context is the matrix element of some local operator between the physical vacuum and a multi-particle
Form Factors of SU(N)\textit{SU}(N)SU(N) Invariant Thirring Model
Smirnov and Zamolodchikov recently introduced a new class of two-dimensional quantum field theories, defined through a differential change of any existing theory by the determinant of the energy-momentum tensor. From this TT‾T\overline{T}TT flow equation one can find a simple expression for both the energy spectrum and the SSS-matrix of the TT‾T\overline{T}TT deformed theories. Our goal is to find the renormalized Lagrangian of the TT‾T\overline{T}TT deformed theories. In the context of the TT‾T\overline{T}TT deformation of an integrable theory, the deformed theory is also integrable and, correspondingly, the SSS-matrix factorizes into two-to-two SSS-matrices. One may thus hope to be able to extract the renormalized Lagrangian from the SSS-matrix. We do this explicitly for the TT‾T\overline{T}TT deformation of a free massive scalar, to second order in the deformation parameter. Once one has the renormalized Lagrangian one can, in principle, compute all other observables, such as correlation functions. We briefly discuss this, as well as the relation between the renormalized Lagrangian, the TT‾T\overline{T}TT flow equation, and the SSS-matrix. We also mention a more general class of integrability-preserving deformations of a free scalar field theory.
Abstract In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field T T ― —constructed out of the components of the stress-energy tensor—and its generalisations—built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices—extensively analysed with the thermodynamic Bethe ansatz—provide the first step in the development of a bootstrap program. In this paper we present a systematic approach to computing matrix elements of operators in generalised T T ― -perturbed models, based on employing the standard form factor program. We show that for theories with diagonal scattering and certain types of fields the deformed form factors, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied.