Parafermionic theory with the symmetry Z_N, for N odd

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

We construct a parafermionic conformal theory with the symmetryZ_N, for N odd, based on the second solution ofFateev-Zamolodchikov for the corresponding parafermionic chiralalgebra. Primary operators are classified according to their transformationproperties under the dihedral group D_N, as singlet, doublet 1,2,...,(N-1)/2, and disorder operators. In an assumed Coulomb gasscenario, the corresponding vertex operators are accommodated by the weightlattice of the Lie algebra B_(N-1)/2. The unitary theories arerepresentations of the cosetSO_n(N) x SO_2(N) / SO_{n+2}(N), with n=1,2,... .Physically, they realise the series of multicritical points instatistical theories having a D_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 odd. Nuclear Physics B, 2003, 664, pp.477. ⟨hal-00000238v2⟩