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

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