Application of a $\mathbb{Z}_{3}$-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices

TL;DR

This paper applies a $ obreak ext{Z}_3$-orbifold method to construct new holomorphic vertex operator algebras of central charge 24 from Niemeier lattices, revealing specific Lie algebra structures in their weight one spaces.

Contribution

It introduces a novel application of Miyamoto's $ obreak ext{Z}_3$-orbifold construction to Niemeier lattice VOAs, producing new examples with predetermined Lie algebra types.

Findings

Constructed holomorphic VOAs with specific Lie algebra structures

Connected VOAs to Schellekens' list entries

Expanded the catalog of known lattice-based VOAs

Abstract

By applying Miyamoto's $\mathbb{Z}_{3}$-orbifold construction to the lattice vertex operator algebras associated to Niemeier lattices and their automorphisms of order 3, we construct holomorphic vertex operator algebras of central charge 24 whose Lie algebras of the weight one spaces are of types $A_{2,3}^6$, $E_{6,3}G_{2,1}^{3}$, and $A_{5,3}D_{4,3}A_{1,1}^{3}$, which correspond to No.6, No.17, and No.32 on Schellekens' list, respectively.