Thick oriented and nonoriented center-vortex $SU(N)$ configurations with fractional topological charge lumps

TL;DR

This paper constructs and analyzes smooth, thick $SU(N)$ center-vortex configurations with mixed orientations, revealing how their complex color structures produce fractional topological charge lumps.

Contribution

It introduces explicit non-Abelian phases in thick vortex configurations, enabling detailed study of their topological charge and fractional lumps beyond previous Abelian or thin vortex models.

Findings

Constructed smooth $SU(N)$ vortex configurations with mixed orientations.

Identified color structures responsible for fractional topological charge lumps.

Visualized the morphology of topological charge density.

Abstract

Mixed oriented and nonoriented center vortices are known to generate nontrivial topological charge. However, most previous analyses have been restricted to Abelian-projected thin configurations. Studies of thick vortices have so far focused on the $SU(2)$ case and on the intersection of a single pair of oriented objects. In this work, we construct mixed oriented and nonoriented thick center-vortex gauge fields in $SU(N)$ with smooth profiles and explicit non-Abelian phases. These phases ensure a smooth interpolation between different Cartan fluxes at monopole junctions. We analyze the resulting topological charge density and visualize its morphology, elucidating the color structures responsible for fractional lumps that together yield a nonvanishing global charge.