Algebraic renormalization of N=2 super Yang-Mills theories coupled to matter

We study the algebraic renormalization of N = 2 Supersymmetric Yang–Mills theories coupled to matter. A regularization procedure preserving both the BRS invariance and the supersymmetry is not known yet, therefore it is necessary to adopt the algebraic method of renormalization, which does not rely on any regularization scheme. The whole analysis is reduced to the solution of cohomology problems arising from the generalized Slavnov operator which summarizes all the symmetries of the model. Besides to unphysical renor- malizations of the quantum fields, we find that the only coupling constant of N = 2 SYMs can get quantum corrections. Moreover we prove that all the symmetries defining the theory are algebraically anomaly–free.