Nonabelian Vortices on Surfaces and Their Statistics

TL;DR

This paper explores the unique properties and quantum statistics of nonabelian vortices on various surfaces within a Yang-Mills-Higgs framework, highlighting differences from planar cases and implications for nonorientable surfaces.

Contribution

It introduces new features of nonabelian vortices on arbitrary surfaces, extending understanding beyond planar geometries and analyzing their quantum statistical behavior.

Findings

Nonabelian vortices exhibit novel behaviors on non-plane surfaces.

Surface topology influences vortex quantum statistics.

Differences arise when the gauge symmetry breaks to a nonabelian subgroup.

Abstract

We discuss the physics of topological vortices moving on an arbitrary surface M in a Yang-Mills-Higgs theory in which the gauge group G breaks to a finite subgroup H. We concentrate on the case where M is compact and/or nonorientable. Interesting new features arise which have no analog on the plane. The consequences for the quantum statistics of vortices are discussed, particularly when H is nonabelian.