The Z_k^(su(2),3/2) Parafermions

TL;DR

This paper introduces a new class of parafermionic models with unique properties, including a novel spectrum and structure constants, and establishes their connection to non-unitary minimal W models, expanding the understanding of conformal field theories.

Contribution

The paper develops a new parafermionic theory with a different spectrum and structure, linking it to known W models and generalizing parafermionic models.

Findings

Defined a new parafermionic model with conformal dimension 3(1-1/k)/2

Calculated structure constants and central charges from associativity

Established equivalence with non-unitary minimal W_k models

Abstract

We introduce a novel parafermionic theory for which the conformal dimension of the basic parafermion is 3(1-1/k)/2, with k even. The structure constants and the central charges are obtained from mode-type associativity calculations. The spectrum of the completely reducible representations is also determined. The primary fields turns out to be labeled by two positive integers instead of a single one for the usual parafermionic models. The simplest singular vectors are also displayed. It is argued that these models are equivalent to the non-unitary minimal W_k(k+1,k+3) models. More generally, we expect all W_k(k+1,k+2 beta) models to be identified with generalized parafermionic models whose lowest dimensional parafermion has dimension beta(1-1/k).