Extrinsic Curvature Dependence of Nielsen-Olesen Strings

TL;DR

This paper develops a collective coordinate approach to describe Nielsen-Olesen vortices in a 3+1D U(1) Higgs model, revealing how extrinsic curvature influences vortex stability and quantum behavior.

Contribution

It introduces a method to derive vortex world-sheet actions incorporating extrinsic curvature effects, especially in the London limit with finite Higgs mass.

Findings

Vortex world-sheets depend on extrinsic curvature in the derived action.

Flat vortex surfaces are stable when coherence length is less than penetration depth.

Quantum vortex configurations are dominated by branched polymers.

Abstract

It is shown how to treat the degrees of freedom of Nielsen-Olesen vortices in the $3+1$-dimensional $U(1)$ higgs model by a collective coordinate method. In the london limit, where the higgs mass becomes infinite, the gauge and goldstone degrees of freedom are integrated out, resulting in the vortex world-sheet action. Introducing an ultraviolet cut-off mimics the effect of finite higgs mass. This action is non-polynomial in derivatives and depends on the extrinsic curvature of the surface. Flat surfaces are stable if the coherence length is less than the penetration depth. It is argued that in the quantum abelian higgs model, vortex world-sheets are dominated by branched polymers.