Einstein billiards and overextensions of finite-dimensional simple Lie algebras

Details Einstein billiards and overextensions of finite-dimensional simple Lie algebras Einstein billiards and overextensions of finite-dimensional simple Lie algebras

2002-06-14

arxiv.org/abs/hep-th/0206125v1

JHEP 0208:030,2002

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, 2 figures

Scientific paper

10.1088/1126-6708/2002/08/030

In recent papers, it has been shown that (i) the dynamics of theories involving gravity can be described, in the vicinity of a spacelike singularity, as a billiard motion in a region of hyperbolic space bounded by hyperplanes; and (ii) that the relevant billiard has remarkable symmetry properties in the case of pure gravity in $d+1$ spacetime dimensions, or supergravity theories in 10 or 11 spacetime dimensions, for which it turns out to be the fundamental Weyl chamber of the Kac-Moody algebras $AE_d$, $E_{10}$, $BE_{10}$ or $DE_{10}$ (depending on the model). We analyse in this paper the billiards associated to other theories containing gravity, whose toroidal reduction to three dimensions involves coset models $G/H$ (with $G$ maximally non compact). We show that in each case, the billiard is the fundamental Weyl chamber of the (indefinite) Kac-Moody ``overextension'' (or ``canonical Lorentzian extension'') of the finite-dimensional Lie algebra that appears in the toroidal compactification to 3 spacetime dimensions. A remarkable feature of the billiard properties, however, is that they do not depend on the spacetime dimension in which the theory is analyzed and hence are rather robust, while the symmetry algebra that emerges in the toroidal dimensional reduction is dimension-dependent.

Affiliated with

Also associated with

No associations

Rating

Einstein billiards and overextensions of finite-dimensional simple Lie algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Einstein billiards and overextensions of finite-dimensional simple Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Einstein billiards and overextensions of finite-dimensional simple Lie algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-98380