Superconformal invariance from N = 2 supersymmetry Ward identities

We algebraically prove the cancellation of the β function at all order of perturbation theory of N = 2 supersymmetric gauge theories with a vanishing one-loop β 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 1⁄2BPS operators. email address: [email protected]