A nonmeromorphic extension of the moonshine module vertex operator algebra

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.