Parafermionic theory with the symmetry ZN, for N odd

We construct a parafermionic conformal theory with the symmetry Z(N), for N odd, based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. Primary operators are classified according to their transformation properties under the dihedral group D-N, as singlet, doublet 1, 2,..., N-1/2, and disorder operators. In an assumed Coulomb gas scenario, the corresponding vertex operators are accommodated by the weight lattice of the Lie algebra B(N-1)/2. The unitary theories are representations of the coset SOn(N) X SO2(N)/SOn+2 (N), with n = 1, 2,.... Physically, they realise the series of multicritical points in statistical theories having a D-N symmetry. (C) 2003 Elsevier B.V. All rights reserved.