Non-Abelian Vortex and Confinement

TL;DR

The paper develops a comprehensive framework for non-Abelian vortices in Higgs-phase gauge theories with $G ightarrow$ a discrete center, showing vortex charges reside in the dual group $ ilde{G}$ (GNO duality) and that sources correspond to weight vectors of dual representations. It provides explicit results for $SU(N)$, $SO(N)$, and $USp(2N)$, detailing minimum fluxes and the dual quantum numbers carried by vortex sources, with special emphasis on $SU(3)$ and the role of Weyl transformations in identifying gauge-equivalent configurations. The analysis connects these non-Abelian vortices to confinement scenarios, arguing that when the magnetic theory is $SU(N)/{Z}_N$, the vortices can realize a non-Abelian dual Meissner effect confining quarks. Appendices illustrate a concrete $SO(3)$ vortex solution and an unwinding gauge transformation for $n=2$, highlighting the topological and gauge-structure subtleties of non-Abelian vortices.

Abstract

We discuss general properties and possible types of magnetic vortices in non-Abelian gauge theories (we consider here $G= SU(N), SO(N), USp(2N)$) in the Higgs phase. The sources of such vortices carry "fractional" quantum numbers such as $Z_n$ charge (for SU(N)), but also full non-Abelian charges of the dual gauge group. If such a model emerges as an effective dual magnetic theory of the fundamental (electric) theory, the non-Abelian vortices can provide for the mechanism of quark-confinement in the latter.

Figures (2)

• Figure 1: A vortex with a higher tension decays into one with a lower tension through the pair production of particles in the adjoint representation.
• Figure 2: The same process as Fig.\ref{['vortex']} seen as a tunnel effect in the semiclassical approximation in the Higgs model.