Fermionic structure in the sine-Gordon model: form factors and null-vectors

TL;DR

This paper demonstrates that two different fermionic descriptions of towers in the sine-Gordon model are equivalent, providing a clearer understanding of the relationship between local fields and form factors in integrable quantum field theory.

Contribution

The authors establish the equivalence of two fermionic frameworks describing towers in the sine-Gordon model, clarifying the connection between local fields and form factors.

Findings

Proved the equivalence of two fermionic descriptions in the sine-Gordon model.

Unified the understanding of towers and local fields in integrable quantum field theory.

Facilitated identification of local fields via fermionic structures.

Abstract

The form factor bootstrap in integrable quantum field theory allows one to capture local fields in terms of infinite sequences of Laurent polynomials called `towers'. For the sine-Gordon model, towers are systematically described by fermions introduced some time ago by Babelon, Bernard and Smirnov. Recently the authors developed a new method for evaluating one-point functions of descendant fields, using yet another fermions which act on the space of local fields. The goal of this paper is to establish that these two fermions are one and the same object. This opens up a way for answering the longstanding question about how to identify precisely towers and local fields.