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# E10 and a "small tension expansion" of M Theory

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### Abstract

A formal small tension'' expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible representations of its SL(10,R) subgroup. We explicitly show how to identify the first four rungs of the E10 coset fields with the values of geometric quantities constructed from D=11 supergravity fields and their spatial gradients taken at some comoving spatial point.

### Most cited references21

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### Supergravity in theory in 11 dimensions

(1978)
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### Oscillatory approach to a singular point in the relativistic cosmology

(2006)
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### Infinite dimensional Lie algebras

(1990)
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### Author and article information

###### Journal
30 July 2002
hep-th/0207267
10.1103/PhysRevLett.89.221601