The W_k structure of the Z_k^(3/2) models

2009/06/04 by Pierre Mathieu, Mathieu, P.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.0906.0949

openalex publication_date 2009/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalized Z_k^(r/2) parafermionic theories - characterized by the dimension (r/2)(1-1/k) of the basic parafermionic field - provide potentially interesting quantum-Hall trial wavefunctions. Such wavefunctions reveal a W_k structure. This suggests the equivalence of (a subclass of) the Z_k^(r/2) models and the W_k(k+1,k+r) ones. This is demonstrated here for r=3 (the gaffnian series). The agreement of the parafermionic and the W spectra relies on the prior determination of the field identifications in the parafermionic case.

Related

• ℤ₃ Parafermionic Chain Emerging From Yang-Baxter Equation
• Characters of graded parafermion conformal field theory
• The Diagonal Affine Coset Construction of the Z_k Parafermion Hall States
• Composing parafermions: a construction of Z_N fractional quantum Hall systems and a modern understanding of confinement and duality
• Integration of the SL(2,R)/U(1) Gauged WZNW Theory by Reduction and Quantum Parafermions