On the Spectral properties of Multi-branes, M2 and M5 branes

Abstract

In this note we summarize some of the properties found in several papers. We characterize spectral properties of the quantum mechanical hamiltonian of theories with fermionic degrees of freedom beyond semiclassical approximation. We obtain a general class of bosonic polynomial potentials for which the Schröedinger 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 also give a sufficient condition for discreteness of the spectrum for supersymmmetric and non supersymmetric theories with a fermionic contribution. We characterize then the spectral properties of different theories: the BMN matrix model, the supermembrane with central charges and a bound state of $N$ D2 with $m$ D0. We show that, while the first two models have a purely discrete spectrum with finite multiplicity, the latter has a continuous spectrum starting from a constant given in terms of the monopole charge.

10pg, Latex, Contributions to the Conference XVI European Workshop on String Theory 2010, Madrid June 14-18, 2010

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Three-Algebras and N=6 Chern-Simons Gauge Theories
• Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
• Spectral properties in supersymmetric matrix models
• The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition
• Intrinsic Moment of Inertia of Membranes as bounds for the mass gap of Yang-Mills Theories
• The discrete spectrum of the D=11 bosonic M5-brane
• Spectral analysis of polynomial potentials and its relation with ABJ/M-type theories