Parafermionic theory with the symmetry ZN for N even

Abstract

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 Z N based on the second solution of Fateev–Zamolodchikov for the corresponding parafermionic chiral algebra. In the present paper we construct the Z N parafermionic theory for N even. Primary operators are classified according to their transformation properties under the dihedral group ( Z N × Z 2, where Z 2 stands for the Z N 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 D N/2 . The unitary theories are representations of the coset SO n ( N)× SO 2( N)/ SO n+2 ( N), with n=1,2,…. We suggest that physically they realise the series of multicritical points in statistical systems having a Z N symmetry.