A nonmeromorphic extension of the moonshine module vertex operator algebra

TL;DR

This paper constructs a nonmeromorphic extension of the moonshine module vertex operator algebra using abelian intertwining algebras, providing new insights into its structure and related superalgebras.

Contribution

It introduces a natural abelian intertwining algebra structure on the Leech lattice VOA and its twisted modules, offering a new proof of the moonshine module's vertex operator algebra structure.

Findings

Established a nonmeromorphic extension of the moonshine module

Identified a vertex operator superalgebra within the structure

Revealed superconformal structures consistent with prior observations

Abstract

We describe a natural structure of an abelian intertwining algebra (in the sense of Dong and Lepowsky) on the direct sum of the untwisted vertex operator algebra constructed {}from the Leech lattice and its (unique) irreducible twisted module. When restricting ourselves to the moonshine module, we obtain a new and conceptual proof that the moonshine module has a natural structure of a vertex operator algebra. This abelian intertwining algebra also contains an irreducible twisted module for the moonshine module with respect to the obvious involution. In addition, it contains a vertex operator superalgebra and a twisted module for this vertex operator superalgebra with respect to the involution which is the identity on the even subspace and is $-1$ on the odd subspace. It also gives the superconformal structures observed by Dixon, Ginsparg and Harvey.