Kac-Moody Algebras and Controlled Chaos

TL;DR

This paper explores how compactification influences chaotic behavior in gravitational systems with p-form matter, linking supergravity models to Kac-Moody algebras and identifying new algebraic structures affecting cosmological chaos.

Contribution

It introduces the concept of algebraic 'mutations' induced by compactification and provides a classification of resulting algebras, including novel Lorentzian examples, in the context of cosmological models.

Findings

Compactification defines algebraic mutations affecting chaos.

New Lorentzian (non-hyperbolic) algebras are identified.

Simple compactifications cannot eliminate chaos in certain string/M-theory models.

Abstract

Compactification can control chaotic Mixmaster behavior in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac-Moody algebras. We show that different compactifications define "mutations" of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi-Yau, or M theory on a manifold of G_2 holonomy.