M2-brane Dynamics in the Classical Limit of the BMN Matrix Model

TL;DR

This paper studies the dynamics of M2-branes in the BMN matrix model's classical limit, identifying finite-energy solutions and analyzing their stability and chaotic behavior in a supersymmetric background.

Contribution

It provides a detailed analysis of ellipsoidal M2-brane solutions and explores their stability, rotation, and chaotic properties within the BMN matrix model framework.

Findings

Finite-energy static and rotating M2-brane solutions identified.

Lyapunov exponents computed for radial fluctuations indicating chaos.

Configurations exhibit bounded angular momentum due to the Myers effect.

Abstract

We investigate the large-N limit of the BMN matrix model by analyzing the dynamics of ellipsoidal M2-branes that spin in the 11-dimensional maximally supersymmetric SO(3)xSO(6) plane-wave background. We identify finite-energy solutions by specifying the local minima of the corresponding energy functional. These configurations are static in SO(3) due to the Myers effect and rotate in SO(6) with an angular momentum that is bounded from above. As a first step towards studying their chaotic properties, we evaluate the Lyapunov exponents of their radial fluctuations.