We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice-punctured torus times a 9D Minkowski spacetime. It corresponds to a M2-brane formulated in 11D space with ten non compact dimensions. The critical points like the poles and the zeros of the fields describing the embedding of the Supermenbrane in the target space are treated rigorously. The nontrivial compactification generates non-trivial mass terms appearing in the bosonic potential, which dominate the full supersymmetric potential and should render the spectrum of the (regularized) Supermembrane discrete with finite multiplicity. The behaviour of the fields around the punctures generate a cosmological term on the Hamiltonian of the theory. The massive supermembrane can also be seen as a nontrivial uplift of a supermembrane torus bundle with parabolic monodromy in 9D. The moduli of the theory is the one associated with the punctured torus, hence it keeps all the nontriviality of the torus moduli even after the decompactification process to ten noncompact dimensions. The formulation of the theory on a punctured torus bundle is characterized by the $(1,1)-knots$ associated to the monodromies.
تحميل البحث