Abstract

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. We do not impose conformal symmetry on the theory since it is not a symmetry of the abelian supermembrane. In distinction, AdS/CFT works with a conformal extension of multiple M2-branes in the low energy approximation. Our theory with the star-product is a full-fledged description of multiple M2-branes minimally immersed. The worldvolume action has (LCG) N = 8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M(9)xT(2) (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N = 8 SYM in the IR phase for any number of M2-branes. We analyze also other limits of the theory.