Parafermionic chiral algebra Z_{3} with the dimension of the principal parafermion fields psi(z), psi^{+}(z), Delta_{psi}=8/3

Abstract

We analyze, and prove, the associativity of the new Z_{3} parafermionic chiral algebra which has been announced some time ago, with principal parafermionic fields having the conformal dimension Δ_ψ=8/3. In doing so we have developed a new method for analyzing the associativity of a given chiral algebra of parafermionic type, the method which might be of a more general significance than a particular conformal field theory studied in detail in this paper. Still, even in the context of our particular chiral algebra, of Z_{3} parafermions with Δ_ψ=8/3, the new method allowed us to give a proof of associativity which we consider to be complete.

115 pages, 3 figures. Some editing of the presentation, corresponds to its published version

References in corpus (5)

• Conformal field theories with Z_N and Lie algebra symmetries
• Parafermionic theory with the symmetry Z_N, for N odd
• Parafermionic theory with the symmetry Z_N, for N even
• Parafermionic theory with the symmetry Z_5
• The third parafermionic chiral algebra with the symmetry Z_{3}

Cited by in corpus (1)

• Two more solutions for the parafermionic chiral algebra Z_{3} with the dimension of the principal parafermionic fields, psi(z), psi^{+}(z), Delta_{psi}=8/3