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#### Higher Order M Theory Corrections and the Kac Moody Algebra E_{10}

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##### Citation

Damour, T., & Nicolai, H. (2005). Higher Order M Theory Corrections and the Kac
Moody Algebra E_{10}.* Classical and Quantum Gravity,* *22*,
2849-2880. doi:10.1088/0264-9381/22/14/003.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4EFE-3

##### Abstract

It has been conjectured that the classical dynamics of M-theory is equivalent to a null geodesic motion in the infinite-dimensional coset space E

_{10}/K(E_{10}), where K(E_{10}) is the maximal compact subgroup of the hyperbolic Kac–Moody group E_{10}. We here provide further evidence for this conjecture by showing that the leading higher-order corrections, quartic in the curvature and related 3-form-dependent terms, correspond to negative imaginary roots of E10. The conjecture entails certain predictions for which higher-order corrections are allowed: in particular corrections of type R^{M}(DF)^{N}are compatible with E_{10}only for M + N = 3k + 1. Furthermore, the leading parts of the R^{4}, R^{7}, ... terms are predicted to be associated with singlets under the decomposition of E_{10}. Although singlets are extremely rare among the 4400 752 653 representations of SL10 appearing in E_{10}up to level l ≤ 28, there are indeed singlets at levels l = 10 and l = 20 which do match with the R^{4}4 and the expected R^{7}corrections. Our analysis indicates a far more complicated behaviour of the theory near the cosmological singularity than suggested by the standard homogeneous ansätze.