Conformal field theories with Z_N and Lie algebra symmetries

Details Conformal field theories with Z_N and Lie algebra symmetries Conformal field theories with Z_N and Lie algebra symmetries

2003-10-10

arxiv.org/abs/hep-th/0310102v1

Phys.Lett. B584 (2004) 186-191

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, 2 figures

Scientific paper

10.1016/j.physletb.2004.01.033

We construct two-dimensional conformal field theories with a Z_N 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 (Z_N x Z_2, where Z_2 stands for the Z_N 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 D_{N/2} when N is even. 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 realize the series of multicritical points in statistical systems having a Z_N symmetry.

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