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

TL;DR

This paper demonstrates that near a cosmological singularity, superstring theory solutions exhibit chaotic oscillations modeled as billiard motions in hyperbolic space, linked to E10 and BE10 algebraic structures, implying a quantum billiard vacuum selection scenario.

Contribution

It establishes a connection between superstring cosmological oscillations and hyperbolic Kac-Moody algebra structures, proving their chaotic nature and proposing a quantum billiard vacuum selection mechanism.

Findings

Chaotic oscillations modeled as billiard motion in hyperbolic space.

Discreteness and arithmetic nature of the Coxeter groups involved.

Implication of a quantum billiard scenario for vacuum selection.

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.