Vortices on the Higgs Branch of the Seiberg-Witten Theory

TL;DR

The paper investigates confinement on the Higgs branch of the Seiberg-Witten SU(2) theory with two fundamental hypermultiplets, showing that Abrikosov-Nielsen-Olesen vortices persist in the limit of vanishing Higgs mass $m_H\to 0$ and form logarithmically thick flux tubes. The authors derive the low-energy Abelian Higgs description on the Higgs branch, construct classical vortex solutions, and compute a non-linear string tension $\tau = 2\pi v^2 / \ln(m_\gamma L)$ leading to a confinement potential $V(L) = \tau L$, where $L$ is the heavy-charge separation. A Wilson-loop generalization and a two-dimensional string representation are developed to argue for the quantum stability of these vortices, and a SUSY-based argument suggests vortices do not destabilize the Higgs branch. The results identify a distinct confinement regime specific to SUSY theories with Higgs branches, characterized by non-linear (log-suppressed) growth of the potential and stable ANO strings on the Higgs branch. The work clarifies how monopole confinement can occur in this setting and highlights the differences from conventional linear confinement.

Abstract

We study the mechanism of confinement via formation of Abrikosov-Nielsen-Olesen vortices on the Higgs branch of N=2 supersymmetric SU(2) gauge theory with massive fundamental matter. Higgs branch represents a limiting case of superconductor of type I with vanishing Higgs mass. We show that in this limit vortices still exist although they become logarithmically "thick". Because of this the confining potential is not linear any longer. It behaves as $L/\log L$ with a distance $L$ between confining heavy charges (monopoles). This new confining regime can occur only in supersymmetric theories. We also address the problem of quantum stability of vortices. To this end we develop string representation for a vortex and use it to argue that vortices remain stable.