Simulating magnetic monopole-defect dynamics

We present simulations of one magnetic monopole interacting with multiple magnetic singularities. Three-dimensional plots of the energy density are constructed from explicit solutions to the Bogomolny equation obtained by Blair, Cherkis, and Durcan. Animations follow trajectories derived from collective coordinate mechanics on the multi-centered Taub-NUT monopole moduli space. We supplement our numerical results with a complete analytic treatment of the single-defect case.

PERIODIC MONOPOLES IN STRING THEORY

Periodic solutions of Bogomolny equation have novel Gravitational Instantons as their moduli spaces. String theory allows to identify these moduli spaces with moduli spaces of Hitchin systems as well as with Coulomb branches of Seiberg-Witten gauge theories on a space with one compact direction. We classify these Gravitatial Instantons. We also perform Nahm transform of Periodic Monopoles establishing the correspondence with Hitchin systems predicted by String Theory.