A(2)2 parafermions: a new conformal field theory Original Research Article

A new parafermionic algebra associated with the homogeneous space A(2)2/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A(2)2 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 W-algebra type primary field with spin two.