Discreteness of the spectrum of the compactified D=11 supermembrane with non-trivial winding

We analyze the Hamiltonian of the compactified D=11 supermembrane with non-trivial central charge in terms of the matrix model constructed recently by some of the authors. Our main result provides a rigorous proof that the quantum Hamiltonian of the supersymmetric model has compact resolvent and thus its spectrum consists of a discrete set of eigenvalues with finite multiplicity.