Vortices on the Higgs Branch of the Seiberg-Witten Theory

TL;DR

This paper investigates vortex formation on the Higgs branch of N=2 supersymmetric SU(2) gauge theory, revealing a novel confining regime with a non-linear potential and demonstrating vortex stability through string representation.

Contribution

It introduces a new confining regime with logarithmic vortex thickness and potential behavior, specific to supersymmetric theories, and develops a string model to analyze vortex stability.

Findings

Vortices exist on the Higgs branch even with vanishing Higgs mass.

Confining potential behaves as L/ log L at large distances.

Vortices are shown to be quantum mechanically stable.

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.