Abstract
We construct two-dimensional conformal field theories with a ZN 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 (ZN×Z2, where Z2 stands for the ZN 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 DN/2 when N is even. The unitary theories are representations of the coset SOn(N)×SO2(N)/SOn+2(N), with n=1,2,…. We suggest that physically they realize the series of multicritical points in statistical systems having a ZN symmetry.
Highlights
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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 DN/2 when N is even
We suggest that physically they realize the series of multicritical points in statistical systems having a ZN symmetry
Summary
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. Conformal field theories with ZN and Lie algebra symmetries We construct two-dimensional conformal field theories with a ZN symmetry, based on the second solution of Fateev-Zamolodchikov for the parafermionic chiral algebra.
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