Truncated Nambu-Poisson Bracket and Entropy Formula for Multiple Membranes

Abstract

We show that there exists a cut-off version of Nambu-Poisson bracket which defines a finite dimensional Lie 3-algebra. The algebra still satisfies the fundamental identity and thus produces N=8 supersymmetric BLG type equation of motion for multiple M2 branes. By counting the number of the moduli and the degree of freedom, we derive an entropy formula which scales as N^{3/2} as expected for the multiple M2 branes.