Model of M-theory with Eleven Matrices

Abstract

We show that an action of a supermembrane in an eleven-dimensional spacetime with a semi-light-cone gauge can be written only with Nambu-Poisson bracket and an invariant symmetric bilinear form under an approximation. Thus, the action under the conditions is manifestly covariant under volume preserving diffeomorphism even when the world-volume metric is flat. Next, we propose two 3-algebraic models of M-theory which are obtained as a second quantization of an action that is equivalent to the supermembrane action under the approximation. The second quantization is defined by replacing Nambu-Poisson bracket with finite-dimensional 3-algebras' brackets. Our models include eleven matrices corresponding to all the eleven space-time coordinates in M-theory although they possess not SO(1,10) but SO(1,2) x SO(8) or SO(1,2) x SU(4) x U(1) covariance. They possess N=1 space-time supersymmetry in eleven dimensions that consists of 16 kinematical and 16 dynamical ones. We also show that the SU(4) model with a certain algebra reduces to BFSS matrix theory if DLCQ limit is taken.

20 pages, references, a table and discussions added, typos corrected

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Cited by in corpus (10)

• Nambu-Sigma model and effective membrane actions
• Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model
• Lie 2-algebra models
• Supersymmetry and DLCQ Limit of Lie 3-algebra Model of M-theory
• Zariski Quantization as Second Quantization
• Extended generalized geometry and a DBI-type effective action for branes ending on branes
• Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes
• Quantum corrections of (fuzzy) spacetimes from a supersymmetric reduced model with Filippov 3-algebra
• On the Structure Constants of Volume Preserving Diffeomorphism Algebra
• A class of hermitian generalized Jordan triple systems and Chern-Simons gauge theory