BPS Monopoles
Paul Sutcliffe
TL;DR
The paper surveys classical BPS monopoles, emphasizing their rich moduli-space geometry, twistor and Nahm descriptions, and slow dynamics via moduli-space metrics. It highlights explicit constructions of multi-monopoles, including axially and Platonic symmetric configurations, and explains how spectral curves, Nahm data, and rational maps encode the solutions. It then extends these ideas to higher-rank gauge groups, exposing simplifications such as countdown cases and Taub–NUT–type metrics in special sectors. Finally, it connects monopoles to S-duality and Seiberg–Witten theory, detailing incarnations in 3D and 4D, exact results on special geodesics, and quantum corrections predicted by duality, thereby linking classical monopole geometry to modern quantum field theory.
Abstract
We review classical BPS monopoles, their moduli spaces, twistor descriptions and dynamics. Particular emphasis is placed upon symmetric monopoles, where recent progress has been made. Some remarks on the role of monopoles in S-duality and Seiberg-Witten theory are also made.