Parafermionic theory with the symmetry ZN, for N odd

Abstract

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 SO n ( N)× SO 2( N)/ SO n+2 ( N), with n=1,2,… . Physically, they realise the series of multicritical points in statistical theories having a D N symmetry.