Hyperbolic Kac Moody Algebras and Chaos in Kaluza Klein Models
By T. Damour, M. Henneaux, B. Julia, H. Nicolai. 2001
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Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinskii, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike (“cosmological”) singularity disappears in spacetime dimensions D ≡ d + 1 > 10. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac–Moody algebra. In this Letter we show that the same connection applies to pure gravity in any spacetime dimension 4, where the relevant algebras are AEd . In this way the disappearance of chaos in pure gravity models in D 11 dimensions becomes linked to the fact that the Kac–Moody algebras AEd are no longer hyperbolic for d 10. 2001 Elsevier Science B.V. All rights reserved.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3e4bfcb8360058b88bd6a6507d4f2d6a6ba79bec
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In Mathematical Physics
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Citations in the corpus
- Cosmological Billiards (2002, background): “A further restriction derives from the fact that the highest weight must be a root of AE3, viz. its square must be smaller or equal to 2: Λ2 = 2 3 (p2 + q2 + pq − ℓ2) ≤ 2 (8.29) Consequently, the representations occurring at level ℓ must belong to the list of all the solutions of (8.28) which are su”