Parafermionic theory with the symmetry ZN for N even Original Research Article

Following our previous papers [Nucl. Phys. B 656 (2003) 259, Nucl. Phys. B 664 (2003) 477] we complete the construction of the parafermionic theory with the symmetry ZN based on the second solution of Fateev–Zamolodchikov for the corresponding parafermionic chiral algebra. In the present paper we construct the ZN parafermionic theory for N even. Primary operators are classified according to their transformation properties under the dihedral group (ZN×Z2, where Z2 stands for the ZN charge conjugation), as two singlets, doublet 1,2,…,N/2−1, and a disorder operator. In an assumed Coulomb gas scenario, the corresponding vertex operators are accommodated by the Kac table based on the weight lattice of the Lie algebra DN/2. The unitary theories are representations of the coset SOn(N)×SO2(N)/SOn+2(N), with n=1,2,…. We suggest that physically they realise the series of multicritical points in statistical systems having a ZN symmetry.