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Abstract: We analyze, and prove, the associativity of the new parafermionic chiral algebra which has been announced some time ago, with principal parafermionic fields having the conformal dimension . In doing so we have developed a new method for analyzing the associativity of a given chiral algebra of parafermionic type, the method which might be of a more general significance than a particular conformal field theory studied in detail in this paper. Still, even in the context of our particular chiral algebra, of parafermions with , the new method allowed us to give a proof of associativity which we consider to be complete. [Copyright &y& Elsevier]

Abstract: Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry , for N odd. New fixed points are found and classified. [Copyright &y& Elsevier]

Abstract: Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry . New fixed points are found and classified. [Copyright &y& Elsevier]

We construct two-dimensional conformal field theories with a ZN symmetry, based on the second solution of Fateev–Zamolodchikov for the parafermionic chiral algebra. Primary operators are classified according to their transformation properties under the dihedral group (ZN×Z2, where Z2 stands for the ZN charge conjugation), as singlets, ⌊(N−1)/2⌋ different doublets, 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 B(N−1)/2 when N is odd, and DN/2 when N is even. The unitary theories are representations of the coset SOn(N)×SO2(N)/SOn+2(N), with n=1,2,… . We suggest that physically they realize the series of multicritical points in statistical systems having a ZN symmetry. [Copyright &y& Elsevier]