Vortices and Flat Connections

TL;DR

This paper determines the structure and volume of the vortex moduli space on a Riemann surface at Bradlow's limit, providing explicit geometric and volume computations and comparing them with general vortex moduli space results.

Contribution

It explicitly characterizes the moduli space of Bogomol'nyi vortices at Bradlow's limit and computes its Kähler form and volume, enhancing understanding of vortex geometry.

Findings

Moduli space is explicitly determined at Bradlow's limit.

Kähler form and volume of the moduli space are computed.

Results are compared with general vortex moduli space findings.

Abstract

At Bradlow's limit, the moduli space of Bogomol'nyi vortices on a compact Riemann surface of genus $g$ is determined. The K\"{a}hler form, and the volume of the moduli space is then computed. These results are compared with the corresponding results previously obtained for a general vortex moduli space.