Curved-space classical solutions of a massive supermatrix model

Abstract

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.

arXiv comment16 pages, no figure, v2: shortened and clarified version, v3: some minor typos corrected

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• Absence of a fuzzy $S^4$ phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model
• Finite N effects on the collapse of fuzzy spheres
• Nonabelian gauge field and dual description of fuzzy sphere
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• Graded Hopf Maps and Fuzzy Superspheres
• Noncommutative geometry, Quantum effects and DBI-scaling in the collapse of D0-D2 bound states
• Fluctuating Fuzzy Funnels
• On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres
• Matrix equations and trilinear commutation relations