Abstract
We algebraically prove the cancellation of the ÎČ function at all order of perturbation theory of = 2 supersymmetric gauge theories with a vanishing one-loop ÎČ function. The proof generalises that recently given for the = 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 ÂœBPS operators.
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