One-loop corrections to the Nielsen-Olesen vortex: collective oscillations

TL;DR

This paper studies the quantum corrections to the Nielsen-Olesen vortex, linking collective string oscillations with translation modes, and derives an effective action consistent with earlier models, including considerations of renormalization.

Contribution

It establishes a connection between translation modes and collective oscillations of the vortex, deriving an effective action and analyzing one-loop corrections.

Findings

Derived an effective action for vortex oscillations.

Connected translation modes with collective string oscillations.

Discussed renormalization aspects of one-loop corrections.

Abstract

We connect the translation modes of the instanton in the two-dimensional Abelian Higgs model with local translations of the vortex of the related model in (3+1) dimensions, the Nielsen-Olesen vortex. In this context these modes describe collective oscillations of the string. We construct the wave function of this mode and we derive, via a virial theorem, an effective action for these oscillations, which is consistent with the action constructed by Nielsen and Olesen using general arguments. We discuss some aspects of renormalization, based on a recent computation of one loop corrections to string tension of the vortex.