Dirac and Seiberg–Witten Monopoles

Abstract

Dirac magnetic monopoles, which may or may not exist in nature, seem to exist everywhere in mathematics. They are in one-to-one correspondence with the natural connections on principal $U(1)$-bundles over $S^2$ and, moreover, appear as solutions to the field equations of $SU(2)$ Yang–Mills–Higgs theory on $\mathfrak{R}^3$ as well as Seiberg–Witten theory and its non-Abelian generalization on Minkowski space-time. This talk will present an informal survey of the situation.