Index theorems and supersymmetry in the soliton sector : (II). Magnetic monopoles in 3+1 dimensions

Abstract

For supersymmetric Yang-Mills theories with Bogomolny-Prasad-Sommerfield monopoles, we use an open-space trace theorem on R³ to calculate the O(h^-) correction to the monopole mass. For the N = 2 theory, the unrenormalized mass correction is non-vanishing (and divergent). To the same order, we calculate the quantum corrections to the central charges, and demonstrate explicitly that the Bogomolny bound is saturated. We also show that the mass correction for the N = 4 theory vanishes to O(h^-). Finally we discuss the renormalization of the mass correction for the N = 2 theory. This requires the parameters of the theory to be renormalized in the monopole background-field gauge, although there is no simple way known to do this. We exhibit calculations in standard gauges to show explicitly that they give gauge-dependent answers. Physical arguments based on the Dirac quantization condition suggest that the renormalized mass correction vanishes.