Generalized Seiberg-Witten equations on Riemann surface

TL;DR

This paper studies generalized Seiberg-Witten equations reduced to Riemann surfaces, revealing a new Higgs field feature and showing the moduli space forms a smooth Kahler manifold with a pre-quantum line bundle.

Contribution

It introduces a novel reduction technique for Seiberg-Witten equations that produces an extra Higgs field and analyzes the geometric structure of the solution moduli space.

Findings

Moduli space is a smooth Kahler manifold.

Construction of a pre-quantum line bundle over the moduli space.

Introduction of an extra Higgs field in the reduced equations.

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 Kahler manifold and construct a pre-quantum line bundle over the moduli space of solutions.