Multiple M2-branes and the Embedding Tensor

TL;DR

This paper demonstrates how the Bagger-Lambert theory for multiple M2-branes can be derived using the embedding tensor approach, unifying it with maximally supersymmetric gauge theories and providing a parity-invariant formulation.

Contribution

It systematically applies the embedding tensor technique to derive the Bagger-Lambert theory and introduces an alternative parity-invariant formulation using scalar fields.

Findings

Bagger-Lambert theory fits into the embedding tensor framework.

The embedding tensor acts as a 3-algebra defining tensor.

A parity-invariant version of the theory is proposed.

Abstract

We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N=8 superconformal theories in 2+1 dimensions. This leads to the Bagger-Lambert theory, with the embedding tensor playing the role of the four-index antisymmetric tensor defining a ``3-algebra''. We present an alternative formulation of the theory in which the embedding tensor is replaced by a set of unrestricted scalar fields. By taking these scalar fields to be parity-odd, the Chern-Simons term can be made parity-invariant.