Representations of $\mathbb{Z}_{2}$-orbifold of the parafermion vertex operator algebra $K(sl_2,k)$

TL;DR

This paper classifies and constructs irreducible modules for the $Z_2$-orbifold subalgebra of the parafermion vertex operator algebra linked to affine Kac-Moody algebra modules, advancing understanding of orbifold VOAs.

Contribution

It provides a complete classification and explicit construction of irreducible modules for the $Z_2$-orbifold of the parafermion VOA associated with $A_1^{(1)}$ at level $k$.

Findings

Classification of irreducible modules achieved

Explicit module constructions provided

Enhanced understanding of orbifold VOAs

Abstract

In this paper, the irreducible modules for the $\mathbb{Z}_{2}$-orbifold vertex operator subalgebra of the parafermion vertex operator algebra associated to the irreducible highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$ of level $k$ are classified and constructed.