Parafermionic theory with the symmetry Z_N, for N even

Vladimir S. Dotsenko (1) , Jesper Lykke Jacobsen (2) , Raoul Santachiara (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

Following our previous papers (hep-th/0212158 and hep-th/0303126) we complete the construction of the parafermionic theory with the symmetry Z_N based onthe 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 latticeof the Lie algebra D_{N/2}. The unitary theories are representations of the coset SO_n(N) x SO_2(N) / SO_{n+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.

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Autre [cond-mat.other]

Vladimir S. Dotsenko, Jesper Lykke Jacobsen, Raoul Santachiara. Parafermionic theory with the symmetry Z_N, for N even. Nuclear Physics B, 2004, 679, pp.464. ⟨hal-00000724⟩