Rotating Central Charge Membranes

TL;DR

This paper derives and analyzes rotating solutions of the supermembrane with central charges on M9×T2, revealing stable classical configurations with discrete spectra and introducing new solutions with a dynamical scalar field.

Contribution

It presents new rotating solutions of the supermembrane with central charges, including solutions with a dynamical scalar field, and connects these to previous models with discrete spectra.

Findings

Rotating solutions satisfy all equations of motion and constraints.

Some solutions correspond to previously known models with discrete spectra.

New solutions include a non-vanishing dynamical scalar field.

Abstract

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 new non-vanishing dynamical scalar field defined on its worldvolume.