Non-perturbative investigations of light bound states of N=1 supersymmetric Yang-Mills theory

In this thesis the light bound states of N = 1 supersymmetric Yang-Mills theory (SYM) with the gauge groups SU(2) and SU(3) are studied in the framework of lattice quantum field theory. SYM is the supersymmetric extension of Yang-Mills theory and it describes the interactions between gluons and their superpartners, the gluinos. Similarly to QCD, SYM is confining at low temperatures. Its lightest bound states form a mass degenerate (chiral) multiplet consisting of three states. Two of these, a scalar and a pseudoscalar state, are mixed states of glueballs and mesons. The third state is a spin-1/2 bound state of gluons and gluinos. Using the variational method in combination with APE and Jacobi smearing we have been able to determine the masses of the ground and first excited states of the chiral multiplet. For this purpose, the techniques to analyze the light states have been systematically optimized leading to a significantly increased precision of the results compared to previous investigations concerning the ground states of SYM with the gauge group SU(2). Supersymmetry is broken by the lattice discretization and thus we have extrapolated the results to the chiral and continuum limit where the symmetry is restored. Indeed, we find the expected mass degeneracies of the ground and first excited states of the chiral supermultiplet. The supersymmetry restoration in the chiral and continuum limit is further supported by the super- symmetric Ward identities, which we have analyzed numerically, and which are fulfilled in this limit. Furthermore, we have quantitatively analyzed the mixing of glueball and meson components of the scalar and pseudoscalar states and we have studied the effect of soft supersymmetry breaking by a non-vanishing gluino mass.