Kac-Moody Algebras and Controlled Chaos
Abstract
Description
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.
4 pages, 2 figures v2: changed terminology (hyperbolic,strictly hyperbolic) --> (Lorentzian,hyperbolic) to accord with standard practice. X"(10) identified as E7^{+++}. References added. v3: Journal version (accepted as a CQG Fast Track Communication)
4 pages, 2 figures v2: changed terminology (hyperbolic,strictly hyperbolic) --> (Lorentzian,hyperbolic) to accord with standard practice. X"(10) identified as E7^{+++}. References added. v3: Journal version (accepted as a CQG Fast Track Communication)