Turbulent aspects of BMN membrane dynamics

TL;DR

This paper studies the dynamics of classical bosonic membranes in the BMN matrix model within an 11-dimensional plane-wave background, revealing turbulence phenomena in membrane stability analysis.

Contribution

It classifies membrane configurations and analyzes their stability, uncovering turbulence and nonlinear instability cascades in the membrane dynamics.

Findings

Identification of membrane configurations in the plane-wave background

Demonstration of turbulence and cascading instabilities

Analysis of stability at multiple perturbation orders

Abstract

We investigate the large-N limit of the BMN matrix model with classical bosonic membranes which have spherical topologies and spin inside the 11-dimensional maximally supersymmetric plane-wave background. First we classify all possible M2-brane configurations based on the distribution of their components inside the SO(3)xSO(6) symmetric plane-wave spacetime. We then formulate a number of simple but very representative ansatzes of dielectric tops that rotate in this space. We examine the leading-order radial and angular/multipole stability for a wide range of these configurations. By analyzing perturbations at the next-to-leading order, we find that they exhibit the phenomenon of turbulent cascading of instabilities. Thereby, long-wavelength perturbations generate higher-order multipole instabilities through their nonlinear couplings.