Rotating Central Charge Membranes

In this work we obtain dynamical solutions of the bosonic sector of the supermembrane theory with central charges formulated on $M_9\times T^2$, denoted by MIM2. The theory with this condition corresponds to a supermembrane with a $C_-$ flux. This sector of the M2-brane is very interesting since classically is stable as it does not contain string-like spikes with zero energy and at quantum level has a purely discrete supersymmetric spectrum. We find rotating solutions of the MIM2 equations of motion fulfilling all of the constraints. By showing that the MIM2 mass operator, contains the mass operator discussed in [Brugues, Rojo, Russo, Nucl. Phys. B 710, 2005] then we show that the rotating solutions previously found in the aforementioned work that also satisfy the topological central charge condition, are solutions of the MIM2. Finally, we find new distinctive rotating membrane solutions that include the presence of a non-vanishing symplectic gauge connection defined on its worldvolume.