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Parafermionic theory with the symmetry Z_N, for N even

Vladimir S Dotsenko·Jesper Lykke Jacobsen·Raoul Santachiara
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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.

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Vladimir S Dotsenko, Jesper Lykke Jacobsen, Raoul Santachiara. 2003-10-14. Parafermionic theory with the symmetry Z_N, for N even. https://doi.org/10.1016/j.nuclphysb.2003.11.019

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