Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms

TL;DR

This paper constructs three new holomorphic vertex operator algebras of central charge 24 using $Z_2$-orbifold methods related to inner automorphisms, expanding the classification of such algebras with specified Lie algebra structures.

Contribution

It introduces novel constructions of holomorphic VOAs with specific Lie algebra structures via orbifold techniques, enriching the understanding of their classification.

Findings

Constructed three new holomorphic VOAs with specified Lie algebras.

Discussed additional constructions of VOAs with different Lie algebra structures.

Expanded the classification of holomorphic VOAs at central charge 24.

Abstract

In this article, we construct three new holomorphic vertex operator algebras of central charge $24$ using the $\mathbb{Z}_2$-orbifold construction associated to inner automorphisms. Their weight one subspaces has the Lie algebra structures $D_{7,3}A_{3,1}G_{2,1}$, $E_{7,3}A_{5,1}$, and $A_{8,3}A_{2,1}^2$. In addition, we discuss the constructions of holomorphic vertex operator algebras with Lie algebras $A_{5,6}C_{2,3}A_{1,2}$ and $D_{6,5}A_{1,1}^2$ from holomorphic vertex operator algebras with Lie algebras $C_{5,3}G_{2,2}A_{1,1}$ and $A_{4,5}^2$, respectively.