On the stability of compactified D = 11 supermembranes: Global aspects of the bosonic sector Original Research Article

We prove that the Hamiltonian for the bosonic sector of D = 11 supermembrane theories, wrapped in an irreducible way around S1 × S1 × M9 on the target manifold, only has strict minima without infinite-dimensional valleys. 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.