Perturbative Beta Function of N=2 Super Yang-Mills Theories
  An algebraic proof of the nonrenormalization theorem for the perturbative beta function of the coupling constant of N=2 Super Yang-Mills theory is provided. The proof relies on a fundamental relationship between the N=2 Yang-Mills action and the local gauge invariant polynomial Tr phi^2, phi(x) being the scalar field of the N=2 vector gauge multiplet. The nonrenormalization theorem for the beta function follows from the vanishing of the anomalous dimension of Tr phi^2. 
A.Blasi, V.E.R.Lemes, N.Maggiore, S.P.Sorella, A.Tanzini, O.S.Ventura,   L.C.Q.Vilar