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

TL;DR

This paper demonstrates that quantum corrections to the N=4 monopole's mass and central charge vanish after infinite composite-operator renormalization, confirming BPS saturation in a finite supersymmetric Yang-Mills theory.

Contribution

It shows that despite nontrivial quantum corrections requiring infinite renormalization, the N=4 monopole remains BPS saturated due to specific improvement terms.

Findings

Quantum corrections are free from anomalous contributions.

Infinite renormalization of operators is necessary for N=4 monopoles.

Quantum BPS saturation is verified after renormalization.

Abstract

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.