  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. The worldvolume action has (LCG) N=8 supersymmetry and it
corresponds to M parallel supermembranes minimally immersed on the target M9xT2
(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.

High Energy Physics - Theory