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

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

2008-01-11

arxiv.org/abs/0801.1829v1

Commun.Num.Theor.Phys.1:453-477,2007

Mathematics

Number Theory

22 pages; published in Comm. Number Theory Phys. 1 (2007), 453-477

Scientific paper

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.

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