Ghost-Free Superconformal Action for Multiple M2-Branes

TL;DR

This paper presents a ghost-free superconformal action for multiple M2-branes by modifying existing theories to eliminate unphysical degrees of freedom, resulting in a consistent and equivalent super Yang--Mills description.

Contribution

It introduces a method to remove ghosts from superconformal M2-brane theories by gauging symmetries, aligning them with super Yang--Mills theories.

Findings

Ghost degrees of freedom are successfully eliminated.

Modified theories are equivalent to N=8 super Yang--Mills.

Preservation of superconformal symmetry after modification.

Abstract

The Bagger--Lambert construction of N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. The SU(N) case is a candidate for the SCFT describing coincident M2-branes. However, these theories contain ghost degrees of freedom, which is unsatisfactory. We modify them by gauging certain global symmetries. This eliminates the ghosts from these theories while preserving all of their desirable properties. The resulting theories turn out to be precisely equivalent to N = 8 super Yang--Mills theories.