Natural constructions of some generalized Kac-Moody algebras as bosonic strings

TL;DR

This paper demonstrates how four specific generalized Kac-Moody algebras can be constructed using bosonic string theory on particular target spaces, assuming the existence of certain vertex operator algebras.

Contribution

It provides a uniform construction method for four generalized Kac-Moody algebras via bosonic strings, under specific algebraic assumptions.

Findings

Four generalized Kac-Moody algebras constructed from bosonic strings.

Construction relies on assumed existence of certain vertex operator algebras.

Identifies conditions under which these algebras can be realized physically.

Abstract

There are 10 generalized Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight on lattices of squarefree level. Under the assumption that the meromorphic vertex operator algebra of central charge 24 and spin-1 algebra $\hat{A}_{p-1,p}^r$ exists we show that four of them can be constructed in a uniform way from bosonic strings moving on suitable target spaces.