Geometric prequantization of a modified Seiberg-Witten moduli space in 2 dimensions

TL;DR

This paper studies a modified version of Seiberg-Witten equations in two dimensions, exploring their solutions and establishing a geometric prequantization of the associated moduli space using symplectic structures and the Quillen determinant line bundle.

Contribution

It introduces a new modification of Seiberg-Witten equations with a different Pauli matrix choice, analyzes their solutions, and constructs a prequantization framework for their moduli space.

Findings

Existence of interesting solutions to the modified equations

Construction of a family of symplectic structures on the moduli space

Prequantization of the moduli space using the Quillen determinant line bundle

Abstract

In this paper we consider a dimensional reduction of slightly modified Seiberg-Witten equations, the modification being a different choice of the Pauli matrices which go into defining the equations. We get interesting equations with a Higgs field, spinors and a connection. We show interesting solutions of these equations. Then we go on to show a family of symplectic structures on the moduli space of these equations which can be geometrically prequantized using the Quillen determinant line bundle.