Multiple M2-branes and Generalized 3-Lie algebras

TL;DR

This paper extends the Bagger-Lambert-Gustavsson model to describe multiple M2-branes using generalized 3-Lie algebras, relaxing antisymmetry constraints and exploring their relation to ordinary Lie algebras.

Contribution

It introduces a generalized class of 3-Lie algebras for M2-brane theories, broadening the algebraic structures beyond total antisymmetry.

Findings

Proposed a generalized superfield formulation for M2-branes.

Identified classes of generalized 3-Lie algebras compatible with gauge invariance.

Connected generalized 3-Lie algebras to ordinary Lie algebras.

Abstract

We propose a generalization of the Bagger-Lambert-Gustavsson action as a candidate for the description of an arbitrary number of M2-branes. The action is formulated in terms of N=2 superfields in three dimensions and corresponds to an extension of the usual superfield formulation of Chern-Simons matter theories. Demanding gauge invariance of the resulting theory does not imply the total antisymmetry of the underlying 3-Lie algebra structure constants. We relax this condition and propose a class of examples for these generalized 3-Lie algebras. We also discuss how to associate various ordinary Lie algebras.