Vortices on the higgs branch of the Seiberg-Witten theory

We study the mechanism of confinement via the formation of Abrikosov-Nielse n-Olesen vortices on the Higgs branch of N = 2 supersymmetric SU(2) gauge t heory with massive fundamental matter. Higgs branch represents a limiting c ase of a superconductor of type I with vanishing Higgs mass. We show that i n this limit vortices still exist although they become logarithmically "thi ck", Because of this the confining potential is not linear any longer. It b ehaves as L/log L with distance L between the confining heavy charges (mono poles). This new confining regime can occur only in supersymmetric theories . We also address the problem of the quantum stability of vortices. To this end we develop a string representation for a vortex and use it to argue th at vortices remain stable. (C) 1999 Elsevier Science B.V. All rights reserv ed.