Orbifolds of Lattice Vertex Operator Algebras at $d=48$ and $d=72$

TL;DR

This paper constructs approximately one hundred new holomorphic vertex operator algebras by examining cyclic orbifolds of extremal even self-dual lattices in dimensions 48 and 72, advancing the understanding of extremal VOAs.

Contribution

It introduces new holomorphic VOAs derived from orbifolds of extremal lattices, expanding the known examples in these dimensions.

Findings

Approximately one hundred new holomorphic VOAs constructed.

Identification of orbifold constructions from extremal lattices.

Enhanced classification of extremal vertex operator algebras.

Abstract

Motivated by the notion of extremal vertex operator algebras, we investigate cyclic orbifolds of vertex operator algebras coming from extremal even self-dual lattices in $d=48$ and $d=72$. In this way we construct about one hundred new examples of holomorphic VOAs with a small number of low weight states.