Z_k String fluxes and monopole confinement in non-Abelian theories

TL;DR

The paper extends the dual Meissner confinement framework to non-Abelian gauge theories by studying N=2 super Yang-Mills with a mass-breaking term. It demonstrates the existence of BPS $Z_k$-strings for arbitrary simple gauge groups and analyzes phase transitions as the mass parameter $m$ is varied, uncovering a regime where monopoles confine via $Z_k$-strings. It derives the precise flux quantization for the strings, shows monopole flux matches string flux, and provides a threshold for string breaking. The results connect non-Abelian confinement to deformations of superconformal theories and discuss potential gauge–string dualities. Practical impact includes deeper insight into non-Abelian confinement mechanisms and topological flux matching in supersymmetric settings.

Abstract

Recently (hep-th/0104171) we considered N=2 super Yang-Mills with a N=2 mass breakingn term and showed the existence of BPS Z_{k}-string solutions for arbitrary simple gauge groups which are spontaneously broken to non-Abelian residual gauge groups. We also calculated their string tensions exactly. In doing so, we have considered in particular the hypermultiplet in the same representation as the one of a diquark condensate. In the present work we analyze some of the different phases of the theory and find that the magnetic fluxes of the monopoles are multiple of the fundamental Z_{k}-string flux, allowing for monopole confinement in one of the phase transitions of the theory. We also calculate the threshold length for a string breaking. Some of these confining theories can be obtained by adding a N=0 deformation term to N=2 or N=4 superconformal theories.