On Some Stability Properties of Compactified D=11 Supermembranes

TL;DR

This paper analyzes the stability of compactified D=11 supermembranes, identifying minimal configurations and showing the absence of infinite valleys at the minima, which has implications for membrane stability in M-theory.

Contribution

It extends previous results by describing all minimal solutions of the bosonic membrane potential on a Riemann surface with arbitrary metric, using 1-forms over a U(1) bundle.

Findings

All minimal solutions are characterized explicitly.

No infinite-dimensional valleys exist at the minima.

Results extend understanding of membrane stability in compactified dimensions.

Abstract

We desribe the minimal configurations of the bosonic membrane potential, when the membrane wraps up in an irreducible way over $S^{1}\times S^{1}$. The membrane 2-dimensional spatial world volume is taken as a Riemann Surface of genus $g$ with an arbitrary metric over it. All the minimal solutions are obtained and described in terms of 1-forms over an associated U(1) fiber bundle, extending previous results. It is shown that there are no infinite dimensional valleys at the minima.