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2008-01-01 - Article/Dans un journal avec peer-review - Anglais - page(s)

Henneaux M., Persson D., Spindel Philippe , "Spacelike Singularities and Hidden Symmetries of Gravity" in Living Rev. Relativity, 11

  • Codes CREF : Mécanique quantique classique et relativiste (DI1211), Théorie quantique des champs (DI1215)
  • Unités de recherche UMONS : Mécanique et gravitation (S884)
Texte intégral :

Abstract(s) :

(Anglais) We review the intimate connection between (super-)gravity close to a spacelike singularity (the \BKL-limit") and the theory of Lorentzian Kac{Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly in nite) sequence of re ections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of in nite-dimensional Kac{Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self- contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the in nite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac{Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.

Notes :
  • (Anglais) http://www.livingreviews.2008-1. e-Print Archive: hep-th/0710.1818
  • (Anglais) Bibliographic Code:2008LRR....11....1H