Prospects of the Nambu Bracket

TL;DR

This paper explores the potential role of the Nambu bracket in M2-brane worldvolume theories, proposing a supersymmetric extension and constructing a superunitary Nambu algebra to complement existing superconformal Chern-Simons formulations.

Contribution

It introduces a supersymmetric generalization of the Nambu bracket and constructs a superunitary Nambu algebra, offering a possible complementary framework for M2-brane theories.

Findings

Constructed the superunitary Nambu algebra.

Analyzed the role of Nambu brackets in supersymmetric theories.

Suggested a complementary approach to superconformal Chern-Simons theory.

Abstract

We review recent progress in formulating the worldvolume theory of M2-branes using the Nambu bracket. Although it is generally agreed that this formulation should be replaced by another using the superconformal Chern-Simons theory, we try to pursue a possible complementary role played by the Nambu bracket. Since the partition function of the superconformal Chern-Simons theory implies a hidden super gauge group, we study the supersymmetric generalization of the Nambu bracket. We explicitly construct the superunitary Nambu algebra.