Z_k String fluxes and monopole confinement in non-Abelian theories

TL;DR

This paper explores Z_k string solutions and monopole confinement in non-Abelian N=2 super Yang-Mills theories, analyzing phases, flux quantization, and string breaking thresholds, with implications for confining theories derived from superconformal models.

Contribution

It provides exact calculations of Z_k string tensions, analyzes monopole flux quantization, and discusses phase transitions and string breaking in non-Abelian supersymmetric gauge theories.

Findings

Monopole magnetic fluxes are multiples of fundamental Z_k-string flux.

Identified phases where monopole confinement occurs.

Calculated the threshold length for string breaking.

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.