  We 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.

High Energy Physics - Theory