Non-Abelian Monopoles, Vortices and Confinement

TL;DR

This paper explores the role of non-Abelian monopoles, vortices, and magnetic quarks in confinement phenomena within supersymmetric and QCD theories, revealing new insights into their properties and the limitations of the sine formula for vortex tensions.

Contribution

It connects semiclassical non-Abelian monopoles to magnetic quarks in supersymmetric QCD and analyzes vortex tension ratios, challenging the universality of the sine formula.

Findings

Magnetic quarks are dominant in certain vacua of softly broken N=2 SQCD.

Vortex tension ratios deviate from the sine formula, indicating it is not universal.

Non-Abelian monopoles relate to magnetic quarks and influence confinement mechanisms.

Abstract

Three closely related issues will be discussed. Magnetic quarks having non-Abelian charges have been found recently to appear as the dominant infrared degrees of freedom in some vacua of softly broken N=2 supersymmetric QCD with SU(n_c) gauge group. Their condensation upon N=1 perturbation causes confinement and dynamical symmetry breaking. We argue that these magnetic quarks can be naturally related to the semiclassical non-Abelian monopoles of the type first discussed by Goddard, Nuyts, Olive and E. Weinberg. We discuss also general properties of non-Abelian vortices and discuss their relevance to the confinement in QCD. Finally, calculation by Douglas and Shenker of the tension ratios for vortices of different N-alities in the softly broken N=2 supersymmetric SU(N) Yang-Mills theory, is carried to the second order in the adjoint multiplet mass. A correction to the ratios violating the sine formula is found, showing that the latter is not a universal quantity.