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We obtain a U(M) action for supermembranes with central charges in the LightCone Gauge (LCG). The theory realizes all of the symmetries and constraints ofthe supermembrane together with the invariance under a U(M) gauge group with Marbitrary. The worldvolume action has (LCG) N=8 supersymmetry and itcorresponds to M parallel supermembranes minimally immersed on the target M9xT2(MIM2). In order to ensure the invariance under the symmetries and to close thecorresponding algebra, a star-product determined by the central chargecondition is introduced. It is constructed with a nonconstant symplectictwo-form where curvature terms are also present. The theory is in the stronglycoupled gauge-gravity regime. At low energies, the theory enters in adecoupling limit and it is described by an ordinary N=8 SYM in the IR phase forany number of M2-branes. We analyze also other limits of the theory: when Mgoes to we obtain a condensate of M2-branes. If we consider, instead of theexact action, its matrix regularized version, for suitable large N but with afinite number of colors, the algebra of the first class-constraints also closeswith the ordinary product and we obtain a regularized 2+1D SU(M) SYM theory inthe IR phase that is coupled to the SU(N) regularized supermembrane action. Thesupersymmetric regularized theory with the ordinary product has purely discretespectrum. Our theory with the star-product is a full-fledged description ofmultiple M2-branes minimally immersed in distinction with other constructionsthat represent multiple M2-branes in the low energy approximation.

A N=8 action for multiple M2-branes with an arbitrary number of colors