Parafermionic quasi-particle basis and fermionic-type characters

Abstract

A new basis of states for highest-weight modules in $\ZZ_k$ parafermionic conformal theories is displayed. It is formulated in terms of an effective exclusion principle constraining strings of $k$ fundamental parafermionic modes. The states of a module are then built by a simple filling process, with no singular-vector subtractions. That results in fermionic-sum representations of the characters, which are exactly the Lepowsky-Primc expressions. We also stress that the underlying combinatorics -- which is the one pertaining to the Andrews-Gordon identities -- has a remarkably natural parafermionic interpretation.

minor modifications and proof in app. C completed; 34 pages (harvmac b)

References in corpus (18)

• Dilogarithm identities
• Fermionic Sum Representations for Conformal Field Theory Characters
• Fermionic Quasi-Particle Representations for Characters of $(G^{(1)}{)}_1\times (G^{(1)}{)}_1ø(G^{(1)}{)}_2$
• Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
• Dilogarithm Identities in Conformal Field Theory
• Spinons in Conformal Field Theory
• Quasi-Particles, Conformal Field Theory, and $q$-Series
• Exclusion Statistics in Conformal Field Theory Spectra
• Spectra in Conformal Field Theories from the Rogers Dilogarithm
• Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz
• Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories
• Spinon basis for higher level SU(2) WZW models
• The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
• Virasoro Characters from Bethe Equations for the Critical Ferromagnetic Three-State Potts Model
• Lift of dilogarithm to partition identities
• Parafermionic character formulae
• Spin-Anisotropy Commensurable Chains: Quantum Group Symmetries and N=2 SUSY
• Generating-function method for fusion rules

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• Graded parafermions: standard and quasi-particle bases
• A quasi-particle description of the M(3,p) models
• SM(2,4k) fermionic characters and restricted jagged partitions
• Paths and partitions: combinatorial descriptions of the parafermionic states
• Parafermionic derivation of Andrews-type multiple sums
• Permutation Orbifold of N=2 Supersymmetric Minimal Models
• Fermionic characters for graded parafermions
• Paths for Z_k parafermionic models
• Fermi-gas interpretation of the RSOS path representation of the superconformal unitary minimal models
• Nonlocal operator basis from the path representation of the M(k+1,k+2) and the M(k+1,2k+3) minimal models
• Permutation Orbifolds in Conformal Field Theories and String Theory
• Local height probabilities in a composite Andrews-Baxter-Forrester model