Metastability of Spherical Membranes in Supermembrane and Matrix Theory

TL;DR

This paper analyzes the stability of rotating ellipsoidal membranes in supermembrane theory, revealing their stability properties, isomorphism with matrix models, and finite boundaries of stability regions.

Contribution

It demonstrates the stability analysis of classical membrane solutions and establishes an isomorphism with SU(N) matrix models for all N.

Findings

Identified stability modes for small deformations.

Established isomorphism with SU(N) matrix equations.

Found finite boundaries for stability regions.

Abstract

Motivated by recent work we study rotating ellipsoidal membranes in the framework of the light-cone supermembrane theory. We investigate stability properties of these classical solutions which are important for the quantization of super membranes. We find the stability modes for all sectors of small multipole deformations. We exhibit an isomorphism of the linearized membrane equation with that of the SU(N) matrix model for every value of $N$. The boundaries of the linearized stability region are at a finite distance and they appear for finite size perturbations.