Non-abelian D=11 Supermembrane

TL;DR

This paper develops a U(M) gauge theory for supermembranes with central charges, revealing a connection to super Yang-Mills theory at low energies and exploring the symmetries and algebraic structures involved.

Contribution

It introduces a novel U(M) supermembrane action with central charges, incorporating a star-product and nonconstant symplectic form, advancing the understanding of supermembrane dynamics.

Findings

The theory exhibits N=8 supersymmetry in Light Cone Gauge.

At low energies, it reduces to N=8 Super Yang-Mills theory.

The star-product ensures symmetry invariance and algebra closure.

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. 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.