Model of M-theory with Eleven Matrices

TL;DR

This paper develops matrix models of M-theory based on supermembrane actions, introducing finite-dimensional 3-algebras that incorporate all eleven spacetime coordinates and exhibit specific symmetries, including supersymmetry.

Contribution

It proposes two novel 3-algebraic models of M-theory derived from supermembrane actions, extending matrix formulations with new algebraic structures and symmetry properties.

Findings

Models include eleven matrices for all spacetime coordinates

Models exhibit N=1 supersymmetry in eleven dimensions

One model reduces to BFSS matrix theory under DLCQ limit

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.