E_{10} Symmetry in One-dimensional Supergravity

Shun'ya Mizoguchi

doi:10.1016/S0550-3213(98)00322-8

paper

E_{10} Symmetry in One-dimensional Supergravity

arXiv:hep-th/9703160 · doi:10.1016/S0550-3213(98)00322-8

Abstract

We consider dimensional reduction of the eleven-dimensional supergravity to less than four dimensions. The three-dimensional $E_{8 (+ 8)} / S O (16)$ nonlinear sigma model is derived by direct dimensional reduction from eleven dimensions. In two dimensions we explicitly check that the Matzner-Misner-type $S L (2, R)$ symmetry, together with the $E_{8}$ , satisfies the generating relations of $E_{9}$ under the generalized Geroch compatibility (hypersurface-orthogonality) condition. We further show that an extra $S L (2, R)$ symmetry, which is newly present upon reduction to one dimension, extends the symmetry algebra to a real form of $E_{10}$ . The new $S L (2, R)$ acts on certain plane wave solutions propagating at the speed of light. To show that this $S L (2, R)$ cannot be expressed in terms of the old $E_{9}$ but truly enlarges the symmetry, we compactify the final two dimensions on a two-torus and confirm that it changes the conformal structure of this two-torus.

33 pages, 3 figures. The action of the Chevalley generators of SL(2,R)_8 is corrected. Commutativity of SL(2,R)_0 and SL(2,R)_8 is checked in detail. The generalized Geroch compatibility (hypersurface-orthogonality) condition is derived

References in corpus (1)

M Theory As A Matrix Model: A Conjecture

E_{10} Symmetry in One-dimensional Supergravity

Abstract

References in corpus (1)

Cited by in corpus (31)