A new construction of the moonshine vertex operator algebra over the real number field

TL;DR

This paper presents a novel construction of the moonshine vertex operator algebra over the real numbers, demonstrating its automorphism group as the Monster group and exploring related VOAs.

Contribution

It introduces a new real-field construction of the moonshine VOA and analyzes its automorphism group and bilinear form, expanding understanding of VOA structures.

Findings

V^{ atural} has a positive definite invariant bilinear form

Full automorphism group of V^{ atural} is the Monster simple group

Constructs infinite series of meromorphic VOAs with finite automorphism groups

Abstract

We give a new construction of the moonshine VOA V^{\natural} over the real number field. We proved that V^{\natural} has a positive definite invariant bilinear form and its full automorphism group is the Monster simple group. We also construct an infinite series of meromorphic VOAs whose full automorphism groups are finite. We calculate the trace form on V^{\natural} for some element of the Monster.