E10 and SO(9,9) invariant supergravity

Details E10 and SO(9,9) invariant supergravity E10 and SO(9,9) invariant supergravity

2004-07-13

arxiv.org/abs/hep-th/0407101v1

JHEP 0407 (2004) 041

Physics

High Energy Physics

High Energy Physics - Theory

1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable by downloading source

Scientific paper

10.1088/1126-6708/2004/07/041

We show that (massive) D=10 type IIA supergravity possesses a hidden rigid SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional reduction to one (time-like) dimension. We explicitly construct the associated locally supersymmetric Lagrangian in one dimension, and show that its bosonic sector, including the mass term, can be equivalently described by a truncation of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a decomposition of E10 under its so(9,9) subalgebra. This decomposition is presented up to level 10, and the even and odd level sectors are identified tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further truncation to the level \ell=0 sector yields a model related to the reduction of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated to the latter, is shown to be a proper subalgebra of E10, in accord with the embedding of type I into type IIA supergravity. The corresponding decomposition of DE10 under so(9,9) is presented up to level 5.

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