2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/199727We algebraically prove the cancellation of the beta function at all order of perturbation theory of N=2 supersymmetric gauge theories with a vanishing one-loop beta function. The proof generalises that recently given for the N=4 case. It uses the consistent Slavnov-Taylor identities of the shadow dependent formulation. We also demonstrate the cancellation at all orders of the anomalous dimensions of vector and hypermultiplet one half BPS operators.17 pagesHigh Energy Physics - Theorytext