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 $SU(3)$ Yang-Mills theory broken to $U(1)\times U(1)$. Both the long distance interactions and the short distance behavior indicate that the moduli space is $R^3\times(R^1 \times {\cal M}_0)/Z$ where ${\cal M}_0$ 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.