アイテム詳細

要旨

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 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 E₁₀ only for M + N = 3k + 1. Furthermore, the leading parts of the R⁴, R⁷, ... terms are predicted to be associated with singlets under the decomposition of E₁₀. Although singlets are extremely rare among the 4400 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 R⁴4 and the expected R⁷ corrections. Our analysis indicates a far more complicated behaviour of the theory near the cosmological singularity than suggested by the standard homogeneous ansätze.