Color superconductivity, BPS strings and monopole confinement in N=2 and N=4 super Yang-Mills theories

TL;DR

This paper reviews recent advances in BPS string solutions and monopole confinement in deformed N=2 and N=4 super Yang-Mills theories, highlighting flux quantization, string breaking thresholds, and Casimir scaling.

Contribution

It provides new insights into the flux structure, stability bounds, and specific configurations of strings and monopoles in these supersymmetric gauge theories.

Findings

Monopole fluxes are integer combinations of string fluxes.

A bound for the string breaking length is established.

In SU(3), string solutions enable three-monopole confining systems.

Abstract

We review some recent developments on BPS string solutions and monopole confinement in the Higgs or (color) superconducting phase of deformed N=2 and N=4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z_N, the BPS string tension satisfies the Casimir scaling law. Furthermore in the SU(3) case the string solutions are such that they allow the formation of a confining system with three monopoles.