Parafermionic theory with the symmetry ZN for N even

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) x 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 SOn(N) X 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 Z(N) symmetry. (C) 2003 Elsevier B.V. All rights reserved.