Two more solutions for the parafermionic chiral algebra Z_{3} with the dimension of the principal parafermionic fields, psi(z), psi^{+}(z), Delta_{psi}=8/3

TL;DR

This paper presents two additional non-minimal solutions for the Z_{3} parafermionic chiral algebra with principal fields of conformal dimension 8/3, expanding the understanding of its algebraic structure.

Contribution

It introduces two new solutions to the Z_{3} parafermionic algebra with specific conformal dimensions, complementing previous work in the series.

Findings

Two non-minimal solutions for the Z_{3} parafermionic algebra

Extensions of the algebraic structure with principal fields of dimension 8/3

Advancement in classification of parafermionic chiral algebras

Abstract

In this paper, which is the second one in a series of two papers, we shall present two more solutions, non-minimal ones, for the Z_{3} parafermionic chiral algebra with Delta_{psi}=Delta_{psi^{+}}=8/3, psi(z), psi^{+}(z) being the principal parafermionic fields.