$A_2^{(2)}$ Parafermions: A New Conformal Field Theory

Abstract

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.

LaTex 19 pages. Version to appear in Nucl. Phys. B

References in corpus (2)

• Twisted $sl(3,\mathbf{C}{)}_k^{(2)}$ Current Algebra: Free Field Representation and Screening Currents
• Twisted Parafermions

Cited by in corpus (3)

• Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra
• The Z_k^(su(2),3/2) Parafermions
• Realizations of Affine Lie Algebra A_^(1) at Negative Levels