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arXiv 0903.5202hep-th
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A N=8 action,用于具有任意数量颜色的多个M2-branes

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

M. P. Garcia del Moral, A. Restuccia

摘要:

在光锥规范(LCG)中,我们得到了具有中心荷的超膜的U(M)作用量.该理论实现了超膜的所有对称性和约束,以及在U(M)规范群下的不变性,其中M是任意的。世界体积作用具有(LCG)N=8超对称性,并且它对应于最小程度地浸没在目标M9 xT 2(MIM 2)上的M个平行超膜。为了保证对称性下的不变性和封闭相应的代数,引入了由中心荷条件决定的星积。它是用一个非常数辛二形式构造的,其中曲率项也存在。该理论是在强耦合规范重力制度。在低能量下,理论进入退耦极限,并且对于任何数量的M2-膜,它都可以用IR阶段的普通N=8 SYM来描述。我们还分析了该理论的其他限制:当M达到时,我们得到了M2-膜的凝聚。如果我们考虑,而不是确切的作用,其矩阵正则化版本,适当的大N,但有限数量的颜色,第一类约束的代数也关闭与普通的产品,我们得到一个正则化的2+ 1维SU(M)SYM理论在IR阶段,耦合到SU(N)正则化超膜作用。具有普通乘积的超对称正则化理论具有纯离散谱。我们的星积理论是对多重M2-膜的一个成熟的描述,它与其他在低能近似下代表多重M2-膜的结构有很大区别。

英文摘要:

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.

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