$A^{(2)}_2$ Parafermions: A New Conformal Field Theory
Xiang-Mao Ding, Mark. D. Gould, Yao-Zhong Zhang
TL;DR
This paper introduces a new conformal field theory based on $A^{(2)}_2$ parafermions, providing free boson representations, energy-momentum tensor realizations, and discovering a novel algebraic structure with a $W$-algebra primary field.
Contribution
It presents the first free boson realization of the $A^{(2)}_2$ parafermion algebra and uncovers a new algebraic structure including a $W$-algebra type primary field.
Findings
Free boson representation with seven fields
Realization of energy-momentum tensor and screening currents
Discovery of a new algebraic structure with a $W$-algebra primary field
Abstract
A new parafermionic algebra associated with the homogeneous space and its corresponding -algebra have been recently proposed. In this paper, we give a free boson representation of the parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a -algebra type primary field with spin two.
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