Monopoles and an identity of Ramanujan

  • Harry Braden (University of Edinburgh, Edinburgh, United Kingdom)
G3 10 (Lecture hall)


Magnetic monopoles, or the topological soliton solutions of Yang-Mills-Higgs gauge theories in three space dimensions, have been objects of fascination for over a quarter of a century. BPS monopoles in particular have been the focus of much research. Many striking results are now known, yet, disappointingly, explicit solutions are rather few. We bring techniques from the study of finite dimensional integrable systems to bear upon the construction. The transcendental constraints of Hitchin may be replaced by (also transcendental) constraints on the period matrix. For a class of curves we show how to these may be reduced to a number theoretic problem. A recently proven result of Ramanujan related to the hypergeometric function enables us to solve these and construct the corresponding monopoles.

Regine Lübke

Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig Contact via Mail

Alexander Bobenko

Technische Universität Berlin

Christian Klein

Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig