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

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.