E10 and a Small Tension Expansion of M Theory

Damour, Thibault; Henneaux, Marc; Nicolai, Hermann

doi:10.1103/PhysRevLett.89.221601

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E10 and a Small Tension Expansion of M Theory

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Nicolai, Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Damour, T., Henneaux, M., & Nicolai, H. (2002). E10 and a Small Tension Expansion of M Theory. Physical Review Letters, 89(22): 221601, pp. 1-4. doi:10.1103/PhysRevLett.89.221601.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-538D-B

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.