On orbifold constructions associated with the Leech lattice vertex operator algebra

TL;DR

This paper investigates orbifold constructions related to the Leech lattice vertex operator algebra and proves the uniqueness of certain holomorphic VOAs based on their weight one Lie algebra structures, offering new construction methods.

Contribution

It demonstrates the uniqueness of specific holomorphic VOAs with given Lie algebra types using reverse orbifold techniques and provides alternative constructions from the Leech lattice VOA.

Findings

Uniqueness of holomorphic VOAs with specified Lie algebra types.

Alternative constructions of these VOAs from the Leech lattice VOA.

Application of reverse orbifold construction to classify VOAs.

Abstract

In this article, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge $24$ is uniquely determined by its weight one Lie algebra if the Lie algebra has the type $A_{3,4}^3A_{1,2}$, $A_{4,5}^2$, $D_{4,12}A_{2,6}$, $A_{6,7}$, $A_{7,4}A_{1,1}^3$, $D_{5,8}A_{1,2}$ or $D_{6,5}A_{1,1}^2$ by using the reverse orbifold construction. Our result also provides alternative constructions of these vertex operator algebras (except for the case $A_{6,7}$) from the Leech lattice vertex operator algebra.