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Eleven dimensional supergravity and the E10/KE10 sigma-model at low A9 levels

T. Damour·H. Nicolai
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Abstract

Recently, the concept of a nonlinear sigma-model over a coset space G/H was generalized to the case where the group G is an infinite-dimensional Kac-Moody group, and H its (formal) `maximal compact subgroup'. Here, we study in detail the one-dimensional (geodesic) sigma-model with G = E10 and H=KE10. We re-examine the construction of this sigma-model and its relation to the bosonic sector of eleven-dimensional supergravity, up to height 30, by using a new formulation of the equations of motion. Specifically, we make systematic use of KE10-orthonormal local frames, in the sense that we decompose the `velocity' on E10/KE10 in terms of objects which are representations of the compact subgroup KE10. This new perspective may help in extending the correspondence between the E10/KE10 sigma-model and supergravity beyond the level currently checked.

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T. Damour, H. Nicolai. 2004-12-12. Eleven dimensional supergravity and the E10/KE10 sigma-model at low A9 levels. https://arxiv.org/abs/hep-th/0410245

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