Quantum mass and central charge of supersymmetric monopoles: Anomalies, current renormalization, and surface terms

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. © SISSA 2006.