Anmerkungen:
Zusammenfassungen in deutscher und englischer Sprache
Beschreibung:
Supersymmetry is one of the possible scenarios for physics beyond the standard model. By introducing a symmetry between bosons and fermions, it might be able to solve several theoretical problems while providing dark matter candidates. As all supersymmetric extensions of the standard model are based on strongly coupled gauge theories, we need non-perturbative methods, to fully investigate them. In this thesis we use lattice calculations, to investigate the two-dimensional N = (2, 2) super Yang-Mills theory, which we derive by a dimensional reduction of the four-dimensional N = 1 super Yang-Mills theory. Unfortunately our lattice formulation breaks supersymmetry explicitly. Thus we devote the first part of the thesis to present the lattice theory and analyze it thoroughly. First we have to discretize Majorana fermions, which leads to a real but not necessarily positive fermion determinant. Second, the classical potential of the scalar fields posses flat directions. Both problems could thwart our lattice simulations. Fortunately, as we demonstrate, both of them are absent in our simulations. At last, we show that the lattice theory posses only one relevant operator, the scalar mass, whose value in the continuum limit is known. The second part of the thesis is devoted to the numerical results. Introducing an additional fine-tuning of the fermion mass, we can reduce the influence of supersymmetry violating terms. Calculating lattice Ward identities, we show the restoration of supersymmetry in the chiral and continuum limit. Finally we calculate the lowlying bound states and extrapolate their masses to the continuum limit. We find two super-multiplets, as predicted from low energy effective theories. The first is the Farrar-Gabadadze-Schwetz super-multiplet which decouples from the theory. The second is the Veneziano-Yankielowicz super-multiplet which becomes massless in the chiral limit. We are further able to estimate the masses of the excited mesons of the latter. They are of the same size as the mass of the gluino-glueball.