Vortices on Orbifolds

TL;DR

This paper explores the properties and mathematical structures of Abelian and non-Abelian vortices on orbifolds using the moduli matrix approach, revealing new geometric and algebraic features.

Contribution

It introduces a novel analysis of vortex moduli spaces on orbifolds, including quiver structures and a half-ADHM construction, expanding understanding of vortex dynamics in these geometries.

Findings

Identification of vortex moduli space structures on orbifolds

Discovery of quiver structures in the Kahler quotient

Derivation of a half-ADHM construction for vortex theory

Abstract

The Abelian and non-Abelian vortices on orbifolds are investigated based on the moduli matrix approach, which is a powerful method to deal with the BPS equation. The moduli space and the vortex collision are discussed through the moduli matrix as well as the regular space. It is also shown that a quiver structure is found in the Kahler quotient, and a half of ADHM is obtained for the vortex theory on the orbifolds as the case before orbifolding.