Abstract
We analyse the outer Dirichlet problem for the Hamiltonian of the SU(N) regularized D = 11 Supermembrane. We show the existence and uniqueness of the solution for this problem. The solution belongs to a suitable Hilbert space, introduced in the present work, which is defined in terms of the supersymmetric charges. The existence and uniqueness of the ground state of the D = 11 supermembrane is directly related to the patching of solutions of the inner and outer Dirichlet problems.
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