Monopole-vortex complex at large distances and nonAbelian duality

TL;DR

This paper analyzes the monopole-vortex complex in a hierarchically broken SU(N+1) gauge theory, revealing how nonAbelian orientational modes endow monopoles with local SU(N) charges through a duality transformation.

Contribution

It introduces a duality framework for the monopole-vortex system, incorporating CP^{N-1} moduli space to describe nonAbelian monopole charges.

Findings

Monopoles act as sources for thin vortices in hierarchical symmetry breaking.

NonAbelian orientational modes propagate along vortices and endow monopoles with SU(N) charges.

Effective CP^{N-1} model describes the monopole-vortex dynamics on a finite worldstrip.

Abstract

We discuss the large-distance approximation of the monopole-vortex complex soliton in a hierarchically broken gauge system, SU(N+1) - > SU(N) x U(1) - > 1, in a color-flavor locked SU(N) symmetric vacuum. The ('t Hooft-Polyakov) monopole of the higher-mass-scale breaking appears as a point and acts as a source of the thin vortex generated by the lower-energy gauge symmetry breaking. The exact color-flavor diagonal symmetry of the bulk system is broken by each individual soliton, leading to nonAbelian orientational CP^{N-1} zeromodes propagating in the vortex worldsheet, well studied in the literature. But since the vortex ends at the monopoles these fluctuating modes endow the monopoles with a local SU(N) charge. This phenomenon is studied by performing the duality transformation in the presence of the CP^{N-1} moduli space. The effective action is a CP^{N-1} model defined on a finite-width worldstrip.