Non-Abelian Superconductors - Lessons from Supersymmetric Gauge Theories for QCD

TL;DR

This paper explores how supersymmetric gauge theories provide insights into QCD confinement and symmetry breaking, highlighting non-abelian monopoles and vortices as key elements in understanding the QCD ground state.

Contribution

It demonstrates that models based on N=2 supersymmetric theories reveal mechanisms of confinement and symmetry breaking relevant to QCD, including the role of non-abelian monopoles and vortices.

Findings

Non-abelian monopoles can dominate infrared dynamics due to quantum effects.

Condensation of monopoles induces confinement and symmetry breaking patterns.

Existence of BPS non-abelian vortices suggests a dual superconductor picture of QCD ground state.

Abstract

Much about the confinement and dynamical symmetry breaking in QCD might be learned from models with supersymmetry. In particular, models based on N=2 supersymmetric theories with gauge groups SU(N), SO(N) and $USp(2 N)$ and with various number of flavors, give deep dynamical hints about these phenomena. For instance, the BPS non-abelian monopoles can become the dominant degrees of freedom in the infrared due to quantum effects. Upon condensation (which can be triggered in these class of models by perturbing them with an adjoint scalar mass) they induce confinement with calculable pattern of dynamical symmetry breaking. This may occur either in a weakly interacting regime or in a strongly coupled regime (in the latter, often the low-energy degrees of freedom contain relatively non-local monopoles and dyons simultaneously and the system is near a nontrivial fixed-point). Also, the existence of sytems with BPS {\it non-abelian vortices} has been shown recently. These results point toward the idea that the ground state of QCD is a sort of dual superconductor of non-abelian variety.