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 = 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 N3/2 as expected for the multiple M2 branes.