We investigate what supersymmetry says about the geometry of the moduli space of hyperbolic monopoles. We construct a three-dimensional supersymmetric Yang-Mills-Higgs theory on hyperbolic space whose half-BPS configurations coincide with (complexified) hyperbolic monopoles. We then study the action of the preserved supersymmetry on the collective coordinates and show that demanding closure of the supersymmetry algebra constrains the geometry of the moduli space of hyperbolic monopoles, turning it into a so-called pluricomplex manifold, thus recovering a recent result of Bielawski and Schwachhöfer.
- Solitons Monopoles and Instantons
- Supersymmetric gauge theory