Quantum Mass and Central Charge of Supersymmetric Monopoles - Anomalies, current renormalization, and surface terms

TL;DR

This paper computes one-loop quantum corrections to the mass and central charge of supersymmetric monopoles, revealing anomaly-induced finite corrections in N=2 but cancellations in N=4, with implications for current renormalization and surface terms.

Contribution

It provides a detailed analysis of quantum corrections to monopole properties, highlighting anomaly effects and the role of surface terms and counterterms in N=2 and N=4 supersymmetric theories.

Findings

Finite anomaly-induced correction to N=2 central charge.

Surface terms cancel via counterterms in N=4 monopoles.

Bulk contributions are nonzero only in N=2 case.

Abstract

We calculate the one-loop quantum corrections to the mass and central charge of N=2 and N=4 supersymmetric monopoles in 3+1 dimensions. The corrections to the N=2 central charge are finite and due to an anomaly in the conformal central charge current, but they cancel for the N=4 monopole. For the quantum corrections to the mass we start with the integral over the expectation value of the Hamiltonian density, which we show to consist of a bulk contribution which is given by the familiar sum over zero-point energies, as well as surface terms which contribute nontrivially in the monopole sector. The bulk contribution is evaluated through index theorems and found to be nonvanishing only in the N=2 case. The contributions from the surface terms in the Hamiltonian are cancelled by infinite composite operator counterterms in the N=4 case, forming a multiplet of improvement terms. These counterterms are also needed for the renormalization of the central charge. However, in the N=2 case they cancel, and both the improved and the unimproved current multiplet are finite.