1. Parafermionic theory with the symmetry Z(N), for N even
- Author
-
Jesper Lykke Jacobsen, Vladimir S. Dotsenko, Raoul Santachiara, Laboratoire de Physique Théorique et Hautes Energies (LPTHE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), and Quantum Condensed Matter Theory (ITFA, IoP, FNWI)
- Subjects
Physics ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,010308 nuclear & particles physics ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,Condensed Matter (cond-mat) ,Current algebra ,FOS: Physical sciences ,Conformal map ,Condensed Matter ,Dihedral group ,01 natural sciences ,High Energy Physics::Theory ,Operator algebra ,High Energy Physics - Theory (hep-th) ,Lattice (order) ,Quantum electrodynamics ,Mathematics::Quantum Algebra ,[PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other] ,0103 physical sciences ,Lie algebra ,Coulomb ,Coset ,010306 general physics ,Mathematical physics - Abstract
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 on the 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 lattice of 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.
- Published
- 2004