On the fermion-boson correspondence for correlation functions of disorder operators

TL;DR

This paper explores the exact correlation functions of disorder operators in 2D quantum field theories, revealing a fermion-boson correspondence and providing a simple derivation using the form factor approach.

Contribution

It demonstrates a clear fermion-boson correspondence for disorder operator correlators and introduces a straightforward derivation method within the form factor framework.

Findings

Correlation functions are inverse for fermionic and bosonic models.

Exact solutions expressed via non-linear differential equations.

Simple derivation of the fermion-boson correspondence in 2D QFT.

Abstract

When a quantum field theory possesses topological excitations in a phase with spontaneously broken symmetry, these are created by operators which are non-local with respect to the order parameter. Due to non-locality, such disorder operators have non-trivial correlation functions even in free massive theories. In two dimensions, these correlators can be expressed exactly in terms of solutions of non-linear differential equations. The correlation functions of the one-parameter family of non-local operators in the free charged bosonic and fermionic models are the inverse of each other. We point out a simple derivation of this correspondence within the form factor approach