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Parafermionic theory with the symmetry Z_N, for N odd

Vladimir S Dotsenko·Jesper Lykke Jacobsen·Raoul Santachiara
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Abstract

We construct a parafermionic conformal theory with the symmetry Z_N, for N odd, based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. Primary operators are classified according to their transformation properties under the dihedral group D_N, as singlet, doublet 1,2,...,(N-1)/2, and disorder operators. In an assumed Coulomb gas scenario, the corresponding vertex operators are accommodated by the weight lattice of the Lie algebra B_(N-1)/2. The unitary theories are representations of the coset SO_n(N) x SO_2(N) / SO_{n+2}(N), with n=1,2,... . Physically, they realise the series of multicritical points in statistical theories having a D_N symmetry.

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Vladimir S Dotsenko, Jesper Lykke Jacobsen, Raoul Santachiara. 2003-05-07. Parafermionic theory with the symmetry Z_N, for N odd. https://doi.org/10.1016/s0550-3213(03)00391-2

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