Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model

TL;DR

This paper develops a comprehensive form factor formula for the O(N) Gross-Neveu model using Bethe Ansatz techniques, validating it through comparisons with 1/N expansion and exploring bound state form factors.

Contribution

It introduces a general form factor formula for the O(N) Gross-Neveu model and proves recursion relations for Bethe Ansatz K-functions, advancing the understanding of exact solutions.

Findings

Form factor formula matches 1/N expansion results

Recursion relations for Bethe Ansatz K-functions established

Bound state form factors analyzed and computed

Abstract

We apply previous results on the O(N) Bethe Ansatz [1 to 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.