Four dimensional supersymmetric Yang-Mills quantum mechanics with three colors

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.

arXiv