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

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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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          Most cited references 9

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          Infinite dimensional Lie algebras

           Victor Kac (1990)
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            A general solution of the Einstein equations with a time singularity

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              Evidence for F-Theory

               Cumrun Vafa (1996)
              We construct compact examples of D-manifolds for type IIB strings. The construction has a natural interpretation in terms of compactification of a 12 dimensional `F-theory'. We provide evidence for a more natural reformulation of type IIB theory in terms of F-theory. Compactification of M-theory on a manifold \(K\) which admits elliptic fibration is equivalent to compactification of F-theory on \(K\times S^1\). A large class of \(N=1\) theories in 6 dimensions are obtained by compactification of F-theory on Calabi-Yau threefolds. A class of phenomenologically promising compactifications of F-theory is on \(Spin(7)\) holonomy manifolds down to 4 dimensions. This may provide a concrete realization of Witten's proposal for solving the cosmological constant problem in four dimensions.
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                Author and article information

                Journal
                19 December 2000
                2001-04-12
                hep-th/0012172 10.1103/PhysRevLett.86.4749
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                Phys.Rev.Lett.86:4749-4752,2001
                4 pages, 1 figure, minor changes in the text, two references added
                hep-th astro-ph gr-qc

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