Form Factors of the Homogeneous Sine-Gordon models

TL;DR

This paper derives determinant formulas for all n-particle form factors in the $SU(3)_2$-homogeneous Sine-Gordon model, confirming theoretical predictions and analyzing the model's behavior across different resonance parameters.

Contribution

It provides explicit determinant formulas for form factors in the $SU(3)_2$-homogeneous Sine-Gordon model, linking them to the c-theorem and thermodynamic Bethe ansatz results.

Findings

Agreement with the thermodynamic Bethe ansatz predictions

Recovery of WZNW-coset central charge at finite resonance

Decoupling into two free fermions at infinite resonance

Abstract

We provide general determinant formulae for all n-particle form factors related to the trace of the energy momentum tensor and the analogue of the order and disorder operator in the $SU(3)_2$-homogeneous Sine-Gordon model. We employ the form factors related to the trace of the energy momentum tensor in the application of the c-theorem and find perfect agreement with the physical picture recently obtained by means of the thermodynamic Bethe ansatz. For finite resonance parameter we recover the expected WZNW-coset central charge and for infinite resonance parameter the theory decouples into two free fermions.