Supersymmetric Yang-Mills (SYM) theories in four dimensions exhibit many interesting non-perturbative phenomena that can be studied by means of Monte Carlo lattice simulations. However, the lattice regularization breaks supersymmetry explicitly, and in general a fine tuning of a large number of parameters is required to correctly extrapolate the theory to the continuum limit. From this perspective, it is important to preserve on the lattice as many symmetries of the original continuum action as possible. Chiral symmetry for instance prevents an additive renormalization of the fermion mass. A (modified) version of chiral symmetry can be preserved exactly if the Dirac operator fulfills the Ginsparg-Wilson relation. In this contribution, we present an exploratory non-perturbative study of N=1 supersymmetric Yang-Mills theory using the overlap formalism to preserve chiral symmetry at non-zero lattice spacings. N=1 SYM is an ideal benchmark toward the extension of our studies to more complex supersymmetric theories, as the only parameter to be tuned is the gluino mass. Overlap fermions allow therefore to simulate the theory without fine-tuning. We compare our approach to previous investigations of the same theory, and we present clear evidences for gluino condensation.
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