Spinning solutions for the bosonic M2-brane with $C_{\pm}$ fluxes

TL;DR

This paper derives classical spinning solutions for the bosonic M2-brane with $C_{\u2212}$ fluxes, revealing stable configurations with discrete spectra and exploring their dualities and physical properties.

Contribution

It introduces new classical spinning membrane solutions with fluxes, including solutions with non-zero symplectic gauge connections, and extends duality relations to these configurations.

Findings

Classical solutions of spinning membranes with fluxes are obtained.

Some solutions include non-zero symplectic gauge connections.

The spectrum remains discrete at quantum level, indicating stability.

Abstract

In this work we obtain classical solutions of the bosonic sector of the supermembrane theory with two-form fluxes associated to a quantized constant $C_{\pm}$ background. This theory satisfies a flux condition on the worldvolume that induces monopoles over it. Classically it is stable as it does not contain string-like spikes with zero energy in distinction with the general case. At quantum level the bosonic membrane has a purely discrete spectrum but the relevance is that the same property holds for its supersymmetric spectrum. We find for this theory spinning membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume in different approximations. By using the duality found between this theory and the so-called supermembrane with central charges, rotating membrane solutions found in that case, are also solutions of the M2-brane with $C_{\pm}$ fluxes. We generalize this result to other embeddings. We find new distinctive rotating membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume. We obtain numerical and analytical solutions in different approximations characterizing the dynamics of the membrane with fluxes $C_{\pm}$ for different ans\"atze of the dynamical degrees of freedom. Finally we discuss the physical admissibility of some of these ans\"atze to model the components of the symplectic gauge field.