Four-dimensional N = 1 supersymmetric Yang-Mills theory on the lattice without fine-tuning

Abstract

We propose a method to formulate four-dimensional N=1 super Yang-Mills theory on the lattice without fine-tuning. We first show that four-dimensional Weyl fermion in a real representation, which is equivalent to Majorana fermion, can be formulated using the domain wall approach with an addition of a Majorana mass term only for the unwanted mirror fermion. This formalism has manifest gauge invariance. Fermion number conservation is violated only by the additional Majorana mass term for the mirror fermion and the violation is propagated to the physical fermion sector through anomalous currents. Due to this feature, the formalism, when applied to the gluino in the present case, ensures the restoration of supersymmetry in the continuum limit without fine-tuning, unlike the proposal by Curci and Veneziano.