In this paper we consider twice-dimensionally reduced, generalized Seiberg-Witten (S-W) equations, defined on a compact Riemann surface. A novel feature of the reduction technique is that the resulting equations produce an extra “Higgs field”. Under suitable regularity assumptions, we show that the moduli space of gauge-equivalent classes of solutions to the reduced equations, is a smooth Kähler manifold and construct a pre-quantum line bundle over the moduli space of solutions.
"Generalized Seiberg-Witten Equations on a Riemann Surface." J. Geom. Symmetry Phys. 45 47 - 66, 2017. https://doi.org/10.7546/jgsp-45-2017-47-66