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

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

2006-01-05

arxiv.org/abs/hep-th/0601029v2

JHEP0606:056,2006

Physics

High Energy Physics

High Energy Physics - Theory

1+40 pages, JHEP style. v2: small corrections and additions, references added

Scientific paper

10.1088/1126-6708/2006/06/056

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.

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