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arXiv · hep-th/0012172

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

Thibault Damour·Marc Henneaux
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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.

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Thibault Damour, Marc Henneaux. 2001-04-12. E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology. https://doi.org/10.1103/physrevlett.86.4749

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