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It has been conjectured that the classical dynamics of M theory is equivalentto 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 groupE10. We here provide further evidence for this conjecture by showing that theleading higher order corrections, quartic in the curvature and relatedthree-form dependent terms, correspond to negative imaginary roots of E10. Theconjecture entails certain predictions for which higher order corrections areallowed: in particular corrections of type R^M (DF)^N are compatible with E10only for M+N=3k+1. Furthermore, the leading parts of the R^4, R^7,... terms arepredicted to be associated with singlets under the SL(10) decomposition of E10.Although singlets are extremely rare among the altogether 4,400,752,653representations of SL(10) appearing in E10 up to level l \leq 28, there areindeed singlets at levels l=10 and l =20 which do match with the R^4 and theexpected R^7 corrections. Our analysis indicates a far more complicatedbehavior of the theory near the cosmological singularity than suggested by thestandard homogeneous ans\"atze.Comment: 45 pages, 1 figur

Higher-order M-theory corrections and the Kac–Moody algebra E 10

Higher-order M-theory corrections and the Kac–Moody algebra E ₁₀