Spectrum of a noncommutative formulation of the D = 11 supermembrane with winding
Mar, 20017 pages
Published in:
- Phys.Rev.D 66 (2002) 045023
e-Print:
- hep-th/0103261 [hep-th]
Report number:
- KCL-MTH-01-06
View in:
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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 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 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 , 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
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