Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories

TL;DR

This paper investigates the nature of electric flux tubes and confinement mechanisms in softly broken N=2 supersymmetric Yang-Mills theories, revealing complex vortex behaviors and phases that differ from standard models.

Contribution

It introduces a modified Abelian Higgs model with off-diagonal couplings, analyzes vortex solutions, and explores the phase structure and string tension ratios in softly broken N=2 theories.

Findings

BPS vortices found at specific parameters

Vortices generally in a hybrid type II phase

Evidence of superconducting string solutions

Abstract

We study the electric flux tubes that undertake color confinement in N=2 supersymmetric Yang-Mills theories softly broken down to N=1 by perturbing with the first two Casimir operators. The relevant Abelian Higgs model is not the standard one due to the presence of an off-diagonal coupling among different magnetic U(1) factors. We perform a preliminary study of this model at a qualitative level. BPS vortices are explicitely obtained for particular values of the soft breaking parameters. Generically however, even in the ultrastrong scaling limit, vortices are not critical but live in a "hybrid" type II phase. Also, ratios among string tensions are seen to follow no simple pattern. We examine the situation at the half Higgsed vacua and find evidence for solutions with the behaviour of superconducting strings. In some cases they are solutions to BPS equations.