D=4 supersymmetric Yang-Mills quantum mechanics with three colors

TL;DR

This paper computes the spectrum of D=4 supersymmetric Yang-Mills quantum mechanics with SU(3) gauge symmetry, revealing discrete spectra in low-fermion sectors and continuous spectra in higher-fermion channels, and analyzes supersymmetry restoration.

Contribution

It provides the first detailed spectral analysis of D=4 SU(3) supersymmetric Yang-Mills quantum mechanics across different fermion sectors.

Findings

Discrete spectrum in sectors with few fermions

Continuous spectrum in sectors with many fermions

Supersymmetry restoration levels vary with cutoff

Abstract

The spectrum of the $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(3)$ gauge group symmetry is computed in different channels with definite total angular momentum and the total number of fermions. In sectors with small number of fermions the spectrum is shown to be purely discrete. Continuous spectrum appears in channels with more fermions. Supersymmetry generators are used to identify supermultiplets and determine the level of restoration of supersymmetry for a finite cutoff.