On orbifold constructions associated with the Leech lattice vertex operator algebra

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 $A_{3,4}^3{A}_{1,2}$, $A_{4,5}^2$, $D_{4,12}{A}_{2,6}$, $A_{6,7}$, $A_{7,4}{A}_{1,1}^3$, $D_{5,8}{A}_{1,2}$ 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.

29 pages

References in corpus (5)

• Modular invariance of trace functions in orbifold theory
• Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24
• A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications
• A Holomorphic vertex operator algebra of central charge 24 with weight one Lie algebra $F_{4,6}{A}_{2,2}$
• Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras

Cited by in corpus (6)

• Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• Cyclic orbifolds of lattice vertex operator algebras having group like fusions
• Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras
• Inertia groups and uniqueness of holomorphic vertex operator algebras
• Lattices, Vertex Algebras and Modular Categories