The classification of extensions of $L_{sl_3}(k,0)$

TL;DR

This paper classifies extensions of the affine vertex operator algebra $L_{sl_3}(k,0)$ using modular invariants, providing a systematic understanding of their structure for positive integer levels.

Contribution

It offers a complete classification of extensions of $L_{sl_3}(k,0)$ based on modular invariants, advancing the understanding of affine vertex operator algebra extensions.

Findings

Classification of extensions for all positive integer levels k

Identification of modular invariants corresponding to each extension

Framework for analyzing similar extensions in other affine VOAs

Abstract

IIn this paper, extensions of affine vertex operator algebras $L_{sl_3}(k,0)$, $k\in \mathbb{Z}_+$, are classified by modular invariants.