Communications in Number Theory and Physics

Volume 1 (2007)

Number 3

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

Pages: 453 – 477



Thomas Creutzig (DESY Theory Group, Hamburg, Germany)

Alexander Klauer (Department of Mathematics, University of Mannheim, Germany)

Nils R. Scheithauer (Maxwell Institute for Mathematical Sciences, University of Edinburgh, Scotland, United Kingdom)


There are 10 generalized Kac–Moody algebras whose denominatoridentities are completely reflective automorphic products ofsingular weight on lattices of squarefree level. Under theassumption that the meromorphic vertex operator algebra ofcentral charge 24 and spin-1 algebra $\hat{A}_{p-1,p}^r$ existswe show that four of them can be constructed in a uniform wayfrom bosonic strings moving on suitable target spaces.

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