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 (g) function follows from the vanishing of the anomalous dimension of Tr phi (2).