Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory

TL;DR

This paper develops a bootstrap fusion approach to derive form-factors for the sausage model, a deformation of the O(3) sigma model, by leveraging analogies with sine-Gordon theory and constructing integral representations.

Contribution

It introduces a free field representation for the sausage model's Zamolodchikov-Faddeev algebra and explains the origin of singularities in bootstrap construction.

Findings

Derived integral representations for form-factors.

Established a relation between sine-Gordon and sausage models.

Clarified the origin of singularities and kinematical poles.

Abstract

We continue the investigation of massive integrable models by means of the bootstrap fusion procedure, started in our previous work on O(3) nonlinear sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear sigma model we prove a similar relation between sine-Gordon theory and a one-parameter deformation of the O(3) sigma model, the sausage model. This allows us to write down a free field representation for the Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral representation for the generating functions of form-factors in this theory. We also clear up the origin of the singularities in the bootstrap construction and the reason for the problem with the kinematical poles.