The third parafermionic chiral algebra with the symmetry Z_{3}

TL;DR

This paper constructs a new parafermionic chiral algebra with Z_{3} symmetry, featuring principal fields of conformal dimension 8/3, expanding the understanding of algebraic structures in conformal field theory.

Contribution

It introduces the third known parafermionic chiral algebra with specific conformal dimensions and Z_{3} symmetry, providing a new example in the field.

Findings

Constructed a new parafermionic algebra with Z_{3} symmetry.

Identified principal fields with conformal dimension 8/3.

Expanded the classification of parafermionic algebras.

Abstract

We have constructed the parafermionic chiral algebra with the principal parafermionic fields \Psi,\Psi^{+} having the conformal dimension \Delta_{\Psi}=8/3 and realizing the symmetry Z_{3}.