Discreteness of the spectrum of the compactified D=11 supermembrane with nontrivial winding

We analyze the Hamiltonian of the compactified D=11 supermembrane with nontrivial central charge in terms of the matrix model constructed in [Phys. Rev. D 66 (2002) 045023, hep-th/0103261]. 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