Algebraic approach to parafermionic conformal field theories

Abstract

Parafermionic conformal field theories are considered on a purely algebraic basis. The generalized Jacobi type identity is presented. Systems of free fermions coupled to each other by nontrivial parafermionic type relations are studied in detail. A new parafermionic conformal algebra is introduced, it describes the sl(2|1)/u(1)^2 coset system.

15 pages; v2: 22 pages, essential modifications, added sections and references; v3: published version, minor modifications, typos fixed

References in corpus (4)

• Generalized Vertex Algebras
• A quasi-particle description of the M(3,p) models
• The Z_k^(su(2),3/2) Parafermions
• The third parafermionic chiral algebra with the symmetry Z_{3}

Cited by in corpus (4)

• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra
• ${\mathbb{Z}}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms
• Z2 x Z2 graded superconformal algebra of parafermionic type