BPS saturation of the N=4 monopole by infinite composite-operator renormalization

Quantum corrections to the magnetic central charge of the monopole in N=4 supersymmetric Yang-Mills theory are free from the anomalous contributions that were crucial for BPS saturation of the two-dimensional supersymmetric kink and the N=2 monopole. However these quantum corrections are nontrivial and they require infinite renormalization of the supersymmetry current, central charges, and energy-momentum tensor, in contrast to N=2 and even though the N=4 theory is finite. Their composite-operator renormalization leads to counterterms which form a multiplet of improvement terms. Using on-shell renormalization conditions the quantum corrections to the mass and the central charge then vanish both, thus verifying quantum BPS saturation.