Parafermionic theory with the symmetry ZN, for N odd Original Research Article

We construct a parafermionic conformal theory with the symmetry ZN, 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 DN, as singlet, doublet 1,2,…,N−12, 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)×SO2(N)/SOn+2(N), with n=1,2,… . Physically, they realise the series of multicritical points in statistical theories having a DN symmetry.