Unstable vortices do not confine

Recently, a geometric model for the confinement of magnetic charges in the context of type II string compactifications was constructed by Greene, Morrison and Vafa [Nucl. Phys. B 481 (1996) 513]. This model assumes the existence of stable magnetic vortices with quantized flux in the low energy theory. However, quantization of flux alone does not imply that the vortex is stable, since the flux may not be confined to a tube of definite size. We show that in the field theoretical model which underlies the geometric model of confinement, static, cylindrically symmetric magnetic vortices do not exist. While our results do not preclude the existence of confinement in a different low-energy regime of string theory, they show that confinement is not a universal outcome of the string picture, and its origin in the low energy theory remains to be understood.