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Publications of the Research Institute for Mathematical Sciences

Form Factors of $\textit{SU}(N)$ Invariant Thirring Model

Yoshihiro Takeyama

Published Mar 31, 2003• 14 citations
Publisher

Abstract

We obtain a new integral formula for solutions of the rational quantum Knizhnik–Zamolodchikov equation associated with Lie algebra \textit{sl}_N at level zero. Our formula contains the integral representation of form factors of \textit{SU}(N) invariant Thirring model constructed by F. Smirnov. We write down recurrence relations arising from the construction of the form factors. We check that the recurrence relations hold for the form factors of the energy momentum tensor.

DOI
10.2977/prims/1145476149

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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

•Jan 1, 1999•2 citations
Form Factors of SU(N)\textit{SU}(N)SU(N) Invariant Thirring Model
We obtain a new integral formula for solutions of the rational quantum Knizhnik–Zamolodchikov equation associated with Lie algebra \textit{sl}_N at level zero. Our formula contains the integral representation of form factors of \textit{SU}(N) invariant Thirring model constructed by F. Smirnov. We write down recurrence relations arising from the construction of the form factors. We check that the recurrence relations hold for the form factors of the energy momentum tensor.
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