Unstable vortices do not confine

TL;DR

This paper demonstrates that static, cylindrically symmetric magnetic vortices are unstable in the considered field theoretical model, challenging assumptions about their role in confinement within certain string theory frameworks.

Contribution

It provides a proof that such magnetic vortices do not exist in the specific low-energy field theory model underlying the geometric confinement model.

Findings

Static, cylindrically symmetric magnetic vortices do not exist in the model.

Flux quantization alone does not guarantee vortex stability.

Confinement may not be a universal feature in string theory models.

Abstract

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. 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.