Comments on the Bagger-Lambert theory and multiple M2-branes

TL;DR

This paper analyzes the Bagger-Lambert superconformal theory for multiple M2-branes, reformulating it for SO(4) gauge group, clarifying parity invariance, and discussing challenges in identifying the correct operators.

Contribution

It provides a reformulation of the Bagger-Lambert theory as an SU(2)  SU(2) gauge theory and discusses key issues like parity invariance and operator construction.

Findings

Reformulation as SU(2)  SU(2) gauge theory clarifies parity invariance.

The scalar potential's zero subspace differs from the M2-brane moduli space.

Identifies difficulties in constructing superconformal primary operators.

Abstract

We study the SO(8) superconformal theory proposed recently by Bagger and Lambert as a possible worldvolume theory for multiple M2-branes. For their explicit example with gauge group SO(4), we rewrite the theory (originally formulated in terms of a three-algebra) as an ordinary SU(2) \times SU(2) gauge theory with bifundamental matter. In this description, the parity invariance of the theory, required for a proper description of M2-branes, is clarified. We describe the subspace of scalar field configurations on which the potential vanishes, and note that this does not coincide with the moduli space for a stack of M2-branes. Finally, we point out a difficulty in constructing the required set of superconformal primary operators which should be present in the correct theory describing multiple M2-branes.