On Superspace Actions for Multiple M2-Branes, Metric 3-Algebras and their Classification

TL;DR

This paper classifies metric 3-algebra structures on matrix algebras and constructs new three-dimensional conformally invariant supersymmetric actions, linking them to known M2-brane theories and algebraic frameworks.

Contribution

It introduces novel metric 3-algebra structures on matrix algebras and develops new conformally invariant N=4 superspace actions related to M2-branes.

Findings

Classified canonical metric 3-algebras on matrix algebras

Constructed new N=4 conformally invariant actions

Connected new actions to Bagger-Lambert-Gustavsson framework

Abstract

We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in N=4 projective superspace based on them. These can be viewed as Chern-Simons theories with special matter content and couplings. We explore the relations of these actions with the N=2 actions based on generalized 3-Lie algebras found earlier and relate them to the original Bagger-Lambert-Gustavsson action.