Non-Perturbative Fine-Tuning in Approximately Supersymmetric Models

We present two Fermi-Bose models with an approximate supersymmetry and which can be solved numerically with great accuracy using the renormalization group method. The bosonic parts of these models consist in Dyson’s hierarchical model with one and two scalar components respectively. We discuss the question of the perturbative cancellations of divergences and compare with the non-perturbative fine-tunings necessary to keep the renormalized scalar mass small in cut-off units. We show evidence for non-perturbative cancellations of quantum corrections, however, we were not able to achieve exact cancellations without fine-tuning.