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

TL;DR

This paper explores the W_k algebra structure in generalized Z_k^(r/2) parafermionic theories, demonstrating their equivalence to certain W_k models, with implications for quantum-Hall wavefunctions.

Contribution

It establishes the equivalence between Z_k^(r/2) parafermionic models and W_k(k+1,k+r) theories for r=3, expanding understanding of their algebraic structures.

Findings

Demonstrated the W_k structure in Z_k^(3/2) models.

Established the equivalence with W_k(k+1,k+3) theories.

Confirmed the agreement of spectra through field identifications.

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.