Lattice Formulation of Supersymmetric Yang-Mills Theories without Fine-Tuning

We present a lattice formulation which gives super Yang-Mills theories in any dimensions with simple supersymmetry as well as extended supersymmetry in the continuum limit without fine-tuning. We first formulate super Yang-Mills theories with simple supersymmetry in 3,4,6,10 dimensions, incorporating the gluino on the lattice using the overlap formalism. In 4D, exact chiral symmetry forbids gluino mass, which ensures that the continuum limit is supersymmetric without fine-tuning. In 3D, exact parity invariance plays the same role. 6D and 10D thories being anomalous, we formulate them as anomalous chiral gauge theories as they are. Dimensional reduction within lattice formulation is then applied to the theories in 3,4,6 and 10D to obtain super Yang-Mills theories in arbitrary dimensions with either simple or extended supersymmetry.