Quantum Stabilization of a Closed Nielsen-Olesen String

TL;DR

This paper demonstrates that quantum effects can stabilize closed Nielsen-Olesen strings in the Abelian Higgs model, preventing their collapse by treating the string radius as a quantum collective coordinate.

Contribution

It introduces a quantum mechanical approach to stabilize closed strings, addressing classical instability issues in the Abelian Higgs model.

Findings

Quantum treatment stabilizes small-radius closed strings.

Classical instability is overcome by quantum effects.

The string's energy remains finite at small radii.

Abstract

We revisit the classical instability of closed strings in the Abelian Higgs model. The instability is expressed by a vanishing energy as the torus-like configuration shrinks to zero size. We treat the radius of the torus as a collective coordinate and demonstrate that a quantum mechanical treatment of this coordinate leads to a stabilization of the closed string at small radii.