Generalized Seiberg-Witten equations on Riemann surface

Abstract

In this paper we consider twice-dimensionally reduced, generalized Seiberg-Witten 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.

Seiberg–Witten monopoles with multiple spinors on a surface times a circle

“…This metric is Kähler because N is the moduli space of solutions of the framed vortex equations (7.1), which is an infinite-dimensional Kähler quotient. For details, see [Per,DT1].…”