Solution of the anomaly puzzle in SUSY gauge theories and the Wilson operator expansion

The present paper completes a series of works on β functions and the anomaly problem in supersymmetric theories. Exact expressions for the β functions are obtained within the framework of standard perturbation theory. The key observation is that the Wilson effective action S_W(μ) does not coincide with the sum of vacuum loops in the external field Γ(μ). The difference is due to infrared effects. The coefficient 1/g² in front of the operator W² in S_W is renormalized only at one-loop level (extension of the non-renormalization theorem for F-terms). This fact results in the one-loop form of the anomalous operator equation for the supercurrent (generalization of the Adler-Bardeen theorem). The full Gell-Mann-Low function emerges after passing to matrix elements of the operators. The quantity entering observable amplitudes differs from 1/g² by Σ_ilnZ_i where the factors Z_i describe renormalization of the fields. (In this sense the Z factors of the matter fields become observable.) We discuss the relation with calculations of the instanton type.