Exploring center vortices in SU(2) and SU(3) relativistic Yang-Mills-Higgs models

TL;DR

This paper develops numerical methods to analyze center vortices in SU(2) and SU(3) Yang-Mills-Higgs models, revealing field profiles, Abelianization regions, and a connection between BPS bounds and N-ality.

Contribution

It introduces numerical tools for solving Yang-Mills-Higgs equations in models with broken SU(N) symmetry and explores their vortex solutions and Abelianization phenomena.

Findings

Field profiles for center vortices in SU(2) and SU(3)

Identification of Abelianization regions in parameter space

A parametrization linking BPS bounds with N-ality

Abstract

We develop numerical tools and apply them to solve the relativistic Yang--Mills--Higgs equations in a model where the SU(N) symmetry is spontaneously broken to its center. In SU(2) and SU(3), we obtain the different field profiles for infinite and finite center vortices, with endpoints at external monopole sources. Exploration of parameter space permits the detection of a region where the equations get Abelianized. Finally, a general parametrization of the color structure of SU(2) fields leads us to a reference point where an Abelian-like BPS bound is reconciled with N-ality.