2009/03/31 by M.P. García del Moral, M. P. Garcia del Moral, A. Restuccia
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Brane cosmology #Central charge #Cosmology and Gravitation Theories #Gauge theory #Geometry #Homogeneous space #Light cone gauge #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Supersymmetry #hep-th
paper · pdf · doi:10.1007/jhep06(2010)020
published as JHEP 1006:020,2010 · 30pg, Latex, Typos corrected, references added, some more explanatory comments
arxiv created 2010/02/21 · openalex publication_date 2010/06/01 · arxiv updated 2011/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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. We analyze also other limits of the theory: when M goes to we obtain a condensate of M2-branes. If we consider, instead of the exact action, its matrix regularized version, for suitable large N but with a finite number of colors, the algebra of the first class-constraints also closes with the ordinary product and we obtain a regularized 2+1D SU(M) SYM theory in the IR phase that is coupled to the SU(N) regularized supermembrane action. The supersymmetric regularized theory with the ordinary product has purely discrete spectrum. Our theory with the star-product is a full-fledged description of multiple M2-branes minimally immersed in distinction with other constructions that represent multiple M2-branes in the low energy approximation.