The proof of the non-renormalization theorem for the gauge anomaly of four-dimensional theories is extended to the case of models with a vanishing one-loop gauge beta function.

Library of Congress Cataloging in Publication Data Piguet, O. (Olivier)Renormalized supersymmetry.

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The complete renormalization procedure of a general N = 1 supersymmetric gauge theory in the Wess-Zumino gauge is presented, using the regulator free "algebraic renormalization" procedure. Both gauge invariance and supersymmetry are included into one single BRS invariance. The form of the general nonabelian anomaly is given. Furthermore, it is explained how the gauge BRS and the supersymmetry functional operators can be extracted from the general BRS operator. It is then shown that the supersymmetry operators actually belong to the closed, finite, Wess-Zumino superalgebra when their action is restricted to the space of the "gauge invariant operators", i.e. to the cohomology classes of the gauge BRS operator.