Four dimensional supersymmetric Yang-Mills quantum mechanics with three colors

TL;DR

This paper investigates the spectrum of four-dimensional supersymmetric Yang-Mills quantum mechanics with SU(2) and SU(3) gauge groups, using numerical methods to identify bound states, spectra, and supersymmetry features.

Contribution

It introduces a detailed numerical approach to analyze the Hamiltonian spectrum of these theories, confirming previous results and exploring supersymmetry restoration at finite cutoff.

Findings

Bound states exist in all channels for SU(2).

Continuous and discrete spectra coexist in the same energy range.

Continuous spectrum shifts to sectors with more fermions in SU(3).

Abstract

The $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(2)$ and $SU(3)$ gauge symmetry groups is studied. A numerical method to find finite matrix representation of the Hamiltonian is presented in detail. It is used to find spectrum of the theory. In the $SU(2)$ case there are bound states in all channels with definite total number of fermions and angular momentum. For 2,3,4 fermions continuous and discrete spectra coexist in the same range of energies. These results are confirmation of earlier studies. With $SU(3)$ gauge group, the continuous spectrum is moved to sectors with more fermions. Supersymmetry generators are used to identify supermultiplets and determine the level of restoration of supersymmetry for a finite cutoff. For both theories, with $SU(2)$ and $SU(3)$ symmetry, wavefunctions are studied and different behavior of bound and scattering states is observed.