Abstract
We obtain a general class of polynomial potentials for which the Schrödinger operator has a discrete spectrum. This class includes all the scalar potentials in membrane, 5-brane, p-branes, multiple M2 branes, BLG and ABJM theories. We provide a proof of the discreteness of the spectrum of the associated Schrödinger operators. This is the first step in order to analyze BLG and ABJM supersymmetric theories from a non-perturbative point of view.
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