Approaching N = 1 Super-Yang-Mills theory with improved lattice actions

Investigations of the non-perturbative effects of N=1 Super-Yang-Mills theory on the lattice are demanding. The lattice breaks translation invariance to a discrete subgroup and consequently also supersymmetry. With a fine-tuning of the Wilson fermions to a critical point, it can be achieved that supersymmetry (as well as chiral symmetry) are restored in the continuum limit. This thesis is intended to contribute to weaken the associated restrictions. Unbroken supersymmetry in the continuum arranges the bound states in supermultiplets. When susy is broken, for example by the lattice discretization, then the mass-degeneracy ends. Based on this observation, we tried to modify the fermionic lattice action to minimize the mass difference of states within a supermultiplet and thus the supersymmetry breaking. The first extension of the Wilson Dirac operator was a clover term. It is known from the Symanzik improvement program that a proper choice of the coefficient reduces the lattice discretization artifacts to the order O(a) in the lattice spacing. There are several possibilities to determine this coefficient and we compared them with a heuristic parameter scan. As an alternative, we added a twisted mass term to the Wilson Dirac operator. When the difference of the untwisted mass parameter to its critical value corresponds to the value of the parity-breaking mass, then the two mesonic partners a- and a-f approach at finite lattice spacing the same mass. After we observed this improvement of the supermultiplet in the numerical data, we also found an analytical proof. Additionally we investigated the eigenvalues of the free Dirac operator with twists in the mass term and the Wilson term. There we found an O(a) improvement when those two terms are orthogonal to each other. With the 45°-mass-twisted Wilson Dirac operator, we performed simulations on a 16^3x32 lattice and analyzed all states of the Veneziano-Yankielowicz and Farrar-Gabadadze-Schwetz supermultiplets