Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories

Details Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories

2009-12-30

arxiv.org/abs/0912.5529v2

Nucl.Phys.B839:112-128,2010

Physics

High Energy Physics

High Energy Physics - Theory

17pg, Latex. Some more explanatory comments and references added.

Scientific paper

10.1016/j.nuclphysb.2010.06.003

We obtain a general class of polynomials for which the Schrodinger 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 Schrodinger operators. This a a first step in order to analyze BLG and ABJM supersymmetric theories from a non-perturbative point of view.

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