Abstract

A regularized model of a noncommutative formulation of the double compactified D=11 supermembrane with nontrivial winding in terms of SU(N) valued maps is obtained. The condition of nontrivial winding is described in terms of a nontrivial line bundle introduced in the formulation of the compactified supermembrane. The multivalued geometrical objects of the model related to the nontrivial wrapping are described in terms of a SU(N) geometrical object, which in the N-->infinity limit converges to the symplectic connection related to the area-preserving diffeomorphisms of the recently obtained noncommutative description of the compactified D=11 supermembrane [I. Martin, J. Ovalle, and A. Restuccia, Phys. Rev. D 64, 096001 (2001)]. The SU(N) regularized canonical Lagrangian is explicitly obtained. The spectrum of the Hamiltonian of the double compactified D=11 supermembrane is discussed. Generically, it contains local string such as spikes with zero energy. However, the sector of the theory corresponding to a principle bundle characterized by the winding number nnot equal0, described by the SU(N) model we propose, is shown to have no local stringlike spikes and hence the spectrum of this sector should be discrete.