A $$ \mathcal{N} = 8 $$ action for multiple M2-branes with an arbitrary number of colors

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 M 9 xT 2 (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 gaugegravity 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: We consider the number of supermembranes going to infinity. All of the symmetries are realized in this case with the ordinary product and they correspond to 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.

The massive supermembrane on a knot

“…It is also possible to consider a conformal deformations of the theory described at low energy by the Super Chern Simons matter theory. A different explicit construction in terms of multiple M2-branes with central charges was presented in [57]. Furthermore, in our construction, the relevant contributions arise from the monodromies around the punctures, where curvature is infinite, hence it does not satisfy the weak curvature hypothesis of [10].…”

Multiple membranes in M-theory

“…[145]. Other multiple M2-brane and ABJM-related literature includes [146][147][148][149][150][151][152].…”

On Chern–simons Quivers and Toric Geometry

“…For a High Energy description (opposite regime to the decoupling limit) of multiple M2-branes with an arbitrary number of colors and without imposing confomality see[15].…”