Truncated Nambu-Poisson Bracket and Entropy Formula for Multiple Membranes

TL;DR

This paper introduces a finite-dimensional truncation of the Nambu-Poisson bracket that maintains key algebraic properties and leads to an entropy scaling consistent with multiple M2 branes, advancing understanding of their algebraic structure.

Contribution

It presents a cut-off version of the Nambu-Poisson bracket forming a finite Lie 3-algebra that supports supersymmetric equations for multiple M2 branes.

Findings

Finite-dimensional Lie 3-algebra satisfying the fundamental identity.

Derivation of an entropy formula scaling as N^{3/2}.

Supports N=8 supersymmetric BLG equations for M2 branes.

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.