Identifying the Operator Content, the Homogeneous Sine-Gordon models

TL;DR

This paper systematically reconstructs the operator content of the $SU(3)_2$-homogeneous Sine-Gordon model using form factors, relating operators via cluster properties and identifying them with conformal field theory counterparts.

Contribution

It provides a systematic construction of all $n$-particle form factors for a broad class of operators in the $SU(3)_2$-homogeneous Sine-Gordon model, including their interrelations and conformal identifications.

Findings

Constructed all $n$-particle form factors for the model.

Analyzed operator relations via momentum space cluster property.

Identified operators with conformal field theory counterparts.

Abstract

We address the general question of how to reconstruct the field content of a quantum field theory from a given scattering theory in the context of the form factor program. For the $SU(3)_2$-homogeneous Sine-Gordon model we construct systematically all $n$-particle form factors for a huge class of operators in terms of general determinant formulae. We investigate how different operators are interrelated by the momentum space cluster property. Finally we compute several two-point correlation functions and carry out the ultraviolet limit in order to identify each operator with its corresponding partner in the underlying conformal field theory.