Spectrum of a noncommutative formulation of the D = 11 supermembrane with winding

Mar, 2001
7 pages
Published in:
  • Phys.Rev.D 66 (2002) 045023
e-Print:
Report number:
  • KCL-MTH-01-06

Citations per year

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Abstract:
A regularized model 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 N\to \infty limit, converges to the symplectic connection related to the area preserving diffeomorphisms of the recently obtained non-commutative description of the compactified D=11 supermembrane.(I. Martin, J.Ovalle, A. Restuccia. 2000,2001) The SU(N) regularized canonical lagrangian is explicitly obtained. In the N N\to \infty limit it converges to the lagrangian in (I.Martin, J.Ovalle, A.Restuccia. 2000,2001) subject to the nontrivial winding condition. The spectrum of the hamiltonian of the double compactified D=11 supermembrane is discussed. Generically, it contains local string like spikes with zero energy. However the sector of the theory corresponding to a principle bundle characterized by the winding number n0n \neq 0, described by the SU(N) model we propose, is shown to have no local string-like spikes and hence the spectrum of this sector should be discrete.
Note:
  • 16 pages.Latex2E
  • 11.10.Kk
  • membrane model
  • supersymmetry
  • symmetry: SU(N)
  • regularization
  • differential forms
  • duality
  • gauge field theory: symplectic
  • gauge field theory: noncommutative
  • Hamiltonian formalism