Weighted Supermembrane Toy Model

TL;DR

This paper introduces a weighted Hilbert space method to analyze zero-energy states in supersymmetric matrix models, demonstrating that the spectrum becomes purely discrete with sufficient weighting, based on eigenvalue bounds.

Contribution

It presents a novel weighted Hilbert space approach and proves spectrum discreteness for a simplified supersymmetric model using eigenvalue bounds.

Findings

Spectrum becomes purely discrete with sufficient weights.

Bound established for negative eigenvalues of matrix Schrödinger operators.

Method simplifies spectral analysis of supersymmetric models.

Abstract

A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights. This follows from a bound for the number of negative eigenvalues of an associated matrix-valued Schr\"odinger operator.