Ghost-Free Superconformal Action for Multiple M2-Branes

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 Bagger and Lambert [1, 2, 3], as well as Gustavsson [4, 5] discovered the general rules for constructing an action for a three-dimensional theory with OSp(8|4) superconformal symmetry. Their solution is based on a 3-algebra, which is characterized by structure constants f ABC D and a metric hAB. The initial assumption was that the