Electromagnetic duality and SU(3) monopoles

Abstract

We consider the low-energy dynamics of a pair of distinct fundamental monopoles that arise in the N = 4 supersymmetric SU(93) Yang-Mills theory broken to U(1) × U(1). Both the long distance interactions and the short distance behavior indicate that the moduli space is R 3 × (R 1 × M 0) Z where M 0 is the smooth Taub-NUT manifold, and we confirm this rigorously. By examining harmonic forms on the moduli space, we find a threshold bound state of two monopoles with a tower of BPS dyonic states built on it, as required by Montonen-Olive duality. We also present a conjecture for the metric of the moduli space for any number of distinct fundamental monopoles for an arbitrary gauge group.