Moduli space volume of vortex and localization

TL;DR

This paper calculates the volume of the moduli space of BPS vortices on a compact Riemann surface using topological field theory and localization, extending previous results to non-Abelian gauge groups and multiple scalar flavors.

Contribution

It introduces a localization-based method to evaluate vortex moduli space volumes, including non-Abelian cases, connecting with the moduli matrix formalism.

Findings

Volume matches previous direct integrations for Abelian vortices

Extension to non-Abelian gauge groups and multiple flavors achieved

Localization results are consistent with moduli matrix formalism

Abstract

Volume of moduli space of BPS vortices on a compact genus h Riemann surface Sigma_h is evaluated by means of topological field theory and localization technique. Vortex in Abelian gauge theory with a single charged scalar field (ANO vortex) is studied first and is found that the volume of the moduli space agrees with the previous results obtained more directly by integrating over the moduli space metric. Next we extend the evaluation to non-Abelian gauge groups and multi-flavors of scalar fields in the fundamental representation. We find that the result of localization can be consistently understood in terms of moduli matrix formalism wherever possible. More details are found in our paper in Prog.Theor.Phys.126 (2011) 637.