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

Abstract

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