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Asymptotic factorization of n-particle SU(N) form factors

Hrachya M. Babujian, Angela Foerster, Michael Karowski

Published Jan 1, 2021• 1 citation
Publisher

Abstract

We investigate the high energy behavior of the SU(N) chiral Gross-Neveu model in 1 + 1 dimensions. The model is integrable and matrix elements of several local operators (form factors) are known exactly. The form factors show rapidity space clustering, which means factorization, if a group of rapidities is shifted to infinity. We analyze this phenomenon for the SU(N) model. For several operators the factorization formulas are presented explicitly.

DOI
10.17169/refubium-31443

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We investigate the high energy behavior of the SU(N) chiral Gross-Neveu model in 1 + 1 dimensions. The model is integrable and matrix elements of several local operators (form factors) are known exactly. The form factors show rapidity space clustering, which means factorization, if a group of rapidities is shifted to infinity. We analyze this phenomenon for the SU(N) model. For several operators the factorization formulas are presented explicitly.
The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral Gross-Neveu model. The vertex operators and Zamolodchikov-Faddeev algebra for the particles are presented, with a similar structure producing a representation of the local operators of the theory. Using these techniques, the form factors of the model are then constructed as traces over the space of Zamolodchikov-Faddeev operators, and given in terms of an integral representation. In particular, the two-particle form factors of the current operator are found, and shown to agree with previous results in the literature.
We apply previous results on the O (N) Bethe Ansatz [1-3] to construct a general form factor formula for the O (N) Gross-Neveu model. We examine this formula for several operators, such as the energy momentum, the spin-field and the current. We also compare these results with the 1/N expansion of this model and obtain full agreement. We discuss bound state form factors, in particular for the three particle form factor of the field. In addition for the two particle case we prove a recursion relation for the K-functions of the higher level Bethe Ansatz.
The purpose of the "bootstrap program" for integrable quantum field theories in 1+1 dimensions is to construct explicitly a model in terms of its Wightman functions.In this article, this program is mainly illustrated in terms of the sinh-Gordon model and the SU (N ) Gross-Neveu model.The nested off-shell Bethe ansatz for an SU (N ) factorizing S-matrix is constructed.We review some previous results on sinh-Gordon form factors and the quantum operator field equation.The problem of how to sum over intermediate states is considered in the short distance limit of the two point Wightman function for the sinh-Gordon model.
The isomorphism SU(4)≃O(6)SU(4) \simeq O(6)SU(4)≃O(6) is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.