Super Yang-Mills Theory on Lattice and the Transformation

A lattice formulation is one of the most powerful tools for a nonperturbative study. We present here a completely new formulation of the super Yang-Mills theory on lattice with an exact fermionic symmetry. There are several pionieering attempts for contructing super Yang-Mills theories on lattice. The first approach, the Wilson fermion and mass finetuning procedure, is a well-simulated method [1,2]. It is based on an observation that, in the perturbative expansion, a gaugino mass is the unique relevant operator which breaks supersymmetry around the SUSY fixed point [1,3]. Nevertheless, nobody knows whether this observation is nonperturbatively correct and there exists the SUSY fixed point in the Wilson fermion theory. Second is an appoach with the staggered fermion [4,5]. This formulation may allow us to have a correspondence between fermion and boson. However, the counting of the degrees of freedom is still difficult for Yang-Mills theory and the full theory has not been constructed until now. Third approach is based on the domain wall fermion [6]. This approach naturally has a vanishing mechanism of the gaugino mass, although, in order to impose a Majorana condition, one must introduce a nonlocal condition along the fifth di-