Higher Order M Theory Corrections and the Kac-moody Algebra E 10

It has been conjectured that the classical dynamics of M theory is equivalent 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. We here provide further evidence for this conjecture by showing that the leading higher order corrections, quartic in the curvature and related three-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 (DF ) are compatible with E10 only for M +N = 3k+1. Furthermore, the leading parts of the R, R, · · · terms are predicted to be associated with singlets under the sl10 decomposition of E10. Although singlets are extremely rare among the altogether 4 400 752 653 representations of sl10 appearing in E10 up to level l ≤ 28, there are indeed singlets at levels l = 10 and l = 20 which do match with the R and the expected R corrections. Our analysis indicates a far more complicated behavior of the theory near the cosmological singularity than suggested by the standard homogeneous ansätze.