On the Stability of Compactified D=11 Supermembranes

TL;DR

This paper proves that certain D=11 supermembrane theories wrapped over specific manifolds have stable minima in their Hamiltonian, characterized by monopole connections and BPS conditions, indicating stability and supersymmetry preservation.

Contribution

It demonstrates the existence of strict Hamiltonian minima for wrapped supermembranes with explicit minimal connections and monopole configurations, advancing understanding of supermembrane stability.

Findings

Supermembrane Hamiltonian has strict minima without valleys.

Minima occur at monopole connections on non-trivial Riemann surfaces.

Minimal maps satisfy BPS condition with half supersymmetry.

Abstract

We prove D=11 supermembrane theories wrapping around in an irreducible way over $S^{1} \times S^{1}\times M^{9}$ on the target manifold, have a hamiltonian with strict minima and without infinite dimensional valleys at the minima for the bosonic sector. The minima occur at monopole connections of an associated U(1) bundle over topologically non trivial Riemann surfaces of arbitrary genus. Explicit expressions for the minimal connections in terms of membrane maps are presented. The minimal maps and corresponding connections satisfy the BPS condition with half SUSY.