Spectral properties in supersymmetric matrix models

TL;DR

This paper establishes a general criterion for the discreteness of spectra in supersymmetric and non-supersymmetric matrix models, enabling comprehensive spectral analysis beyond semiclassical approximations.

Contribution

It introduces a new sufficiency criterion for spectral discreteness applicable to complete Hamiltonians, advancing spectral analysis in matrix models.

Findings

BMN model has a discrete spectrum

Supermembrane regularizations also have discrete spectra

D2-D0 bound state exhibits a continuous spectrum with a monopole charge lower bound

Abstract

We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-su-persymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.