E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology

Abstract

It is shown that the never ending oscillatory behaviour of the generic solution, near a cosmological singularity, of the massless bosonic sector of superstring theory can be described as a billiard motion within a simplex in 9-dimensional hyperbolic space. The Coxeter group of reflections of this billiard is discrete and is the Weyl group of the hyperbolic Kac-Moody algebra E${}_{10}$ (for type II) or BE${}_{10}$ (for type I or heterotic), which are both arithmetic. These results lead to a proof of the chaotic (``Anosov'') nature of the classical cosmological oscillations, and suggest a ``chaotic quantum billiard'' scenario of vacuum selection in string theory.

4 pages, 1 figure, minor changes in the text, two references added

References in corpus (1)

• On the Covariance of the Mixmaster Chaoticity

Cited by in corpus (116)

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