Lattice Formulation of Supersymmetric Yang–mills Theories Without Fine Tuning

We consider an application of the overlap formalism to supersymmetric Yang–Mills theory in three dimensions. We extend the overlap formalism for 3D Dirac fermion to Majorana fermion and show that the parity invariance is exactly preserved, which ensures that the continuum limit is supersymmetric without fine tuning. For SU (N) gauge group, N must be taken to be even in order to make the theory free from global gauge anomaly. We also discuss how to obtain two-dimensional super Yang–Mills theory from the 3D theory through dimensional reduction on the lattice.