We investigate here a supermatrix model with a mass term and a cubic interaction. It is based on the super Lie algebra osp(1|32,R), which could play a role in the construction of the eleven-dimensional M-theory. This model contains a massive version of the IIB matrix model, where some fields have a tachyonic mass term. Therefore, the trivial vacuum of this theory is unstable. However, this model possesses several classical solutions where these fields build noncommutative curved spaces and these solutions are shown to be energetically more favorable than the trivial vacuum. In particular, we describe in details two cases, the SO(3) \times SO(3) \times SO(3) (three fuzzy 2-spheres) and the SO(9) (fuzzy 8-sphere) classical backgrounds.Comment: 16 pages, no figure, v2: shortened and clarified version, v3: some minor typos correcte
Taking seriously the hypothesis that the full symmetry algebra of M-theory is osp(1|32, R), we derive the supersymmetry transformations for all fields that appear in 11-and 12dimensional realizations and give the associated SUSY algebras. We study the backgroundindependent osp(1|32, R) cubic matrix model action expressed in terms of representations of the Lorentz groups SO(10, 2) and SO(10, 1). We explore further the 11-dimensional case and compute an effective action for the BFSS-like degrees of freedom. We find the usual BFSS action with additional terms incorporating couplings to transverse 5-branes, as well as a mass-term and an infinite tower of higher-order interactions.
We study T 11−D−q × T q / n orbifold compactifications of eleven-dimensional supergravity and M-theory using a purely algebraic method. Given the description of maximal supergravities reduced on square tori as non-linear coset σ-models, we exploit the mapping between scalar fields of the reduced theory and directions in the tangent space over the coset to construct the orbifold action as a non-Cartan preserving finite order inner automorphism of the complexified U-duality algebra. Focusing on the exceptional serie of Cremmer-Julia groups, we compute the residual U-duality symmetry after orbifold projection and determine the reality properties of their corresponding Lie algebras. We carry out this analysis as far as the hyperbolic e 10 algebra, conjectured to be a symmetry of M-theory. In this case the residual subalgebras are shown to be described by a special class of Borcherds and Kac-Moody algebras, modded out by their centres and derivations. Furthermore, we construct an alternative description of the orbifold action in terms of equivalence classes of shift vectors, and, in D = 1, we show that a root of e 10 can always be chosen as the class representative. Then, in the framework of the E 10|10 /K(E 10|10 ) effective σ-model approach to M-theory near a spacelike singularity, we identify these roots with brane configurations stabilizing the corresponding orbifolds. In the particular case of 2 orbifolds of M-theory descending to type 0' orientifolds, we argue that these roots can be interpreted as pairs of magnetized D9-and D9'-branes, carrying the lower-dimensional brane charges required for tadpole cancellation. More generally, we provide a classification of all such roots generating n product orbifolds for n 6, and hint at their possible interpretation. 12 Conclusion 95 A Highest roots, weights and the Matrix R 99 B The U-duality group for 11D supergravity 100 C Conventions and involutive automorphisms for the real form so(8, 6) 101
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