Free field representation for the O(3) nonlinear sigma model and bootstrap fusion

TL;DR

This paper explores a free field representation for the O(3) nonlinear sigma model using bootstrap fusion, enabling new solutions for form-factor equations similar to those in sine-Gordon models.

Contribution

It develops a free field representation for the O(3) sigma model's algebra and form-factor solutions, extending methods used in sine-Gordon and SU(2) Thirring models.

Findings

Constructed a free field representation for the O(3) Zamolodchikov-Faddeev algebra.

Derived form-factor solutions analogous to those in sine-Gordon models.

Discussed potential extensions to other integrable models.

Abstract

The possibility of the application of the free field representation developed by Lukyanov for massive integrable models is investigated in the context of the O(3) sigma model. We use the bootstrap fusion procedure to construct a free field representation for the O(3) Zamolodchikov- Faddeev algebra and to write down a representation for the solutions of the form-factor equations which is similar to the ones obtained previously for the sine-Gordon and SU(2) Thirring models. We discuss also the possibility of developing further this representation for the O(3) model and comment on the extension to other integrable field theories.