Spectral properties in supersymmetric matrix models

Abstract

We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric 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. Crown

Eigenvalues of Supersymmetric Quantum Matrix Models

“…The slowest convergence rate is observed for supersymmetric model with two flat directions, slightly better convergence is found for model with one flat direction, and for remaining two models with discrete levels, convergence rate is very fast, similar to those observed for onedimensional cases studied in [10]. (17) without any flat direction, [12] for various dimension N of x and p matrices.…”

“…3) as has been already shown on this and related supersymmetric models [12][13][14][15][16][17][18][19][20]. One can predict the energy of the ground state as a function of the number of basis functions with very high accuracy, but in any concrete numerical calculation (using a finite basis) it cannot be expected to get zero energy, unless the limiting case of infinite basis is considered [16].…”

“…As has been shown [12], a model without flat directions (potential x 2 (y + 1) 2 + y 2 in direction (x → ∞, y = −1) remains equal to 1) has a non-empty continuous spectrum comprising the interval [1, ∞) (Fig. 4), moreover, there is a ground state with energy ∼ 0.8 below the bottom of the essential spectrum.…”

“…(17) with eigenvalue space spanned by interval [1, ∞]. There is also ground state eigenvalue below E 1 as reported in [12]. Convergence rates of ground state energy for all studied models are summarized in Fig.…”

“…This supersymmetric x 2 y 2 model has two flat directions (x, 0) and (0, y). In a recent study [12], one flat direction has been eliminated using potential V (x, y) = x 2 y 2 + y 2 .…”