Compactification of the moduli spaces of vortices and coupled vortices

TL;DR

This paper establishes an analytic compactification of the moduli spaces of vortices and coupled vortices on compact Kähler manifolds, introducing ideal coupled vortices and analyzing their singularities.

Contribution

It introduces the concept of ideal coupled vortices and characterizes their singularities, extending the understanding of moduli spaces in gauge theory.

Findings

Established an analytic compactification of vortex moduli spaces

Introduced and characterized ideal coupled vortices

Connected singularities of coupled vortices to Hermitian-Yang-Mills connections

Abstract

Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of the moduli spaces of vortices and coupled vortices on hermitian vector bundles over compact K\"ahler manifolds. In doing so we introduced the concept of ideal coupled vortices and characterized the singularities of ideal coupled vortices as well as Hermitian-Yang-Mills connections.