Expansion in the Width: the Case of Vortices

TL;DR

This paper develops an approximate solution for curved vortices in the Abelian Higgs model, revealing complex zero structures and trajectories that differ from classical Nambu-Goto predictions.

Contribution

It introduces a first-order approximate solution for curved vortices using the Hilbert-Chapman-Enskog method and analyzes the zero structure and trajectories of the Higgs field.

Findings

Higgs field zeros can split into multiple points with different orders.

Zero trajectories can deviate from Nambu-Goto type paths.

For topological charge n≥2, zeros of different orders follow distinct trajectories.

Abstract

We construct an approximate solution of field equations in the Abelian Higgs model which describes motion of a curved vortex. The solution is found to the first order in the inverse mass of the Higgs field with the help of the Hilbert-Chapman-Enskog method. Consistency conditions for the approximate solution are obtained with the help of a classical Ward identity. We find that the Higgs field of the curved vortex of the topological charge $n \geq 2$ in general does not have single n-th order zero. There are two zeros: one is of the (n-1)-th order and it follows a Nambu-Goto type trajectory, the other one is of the first order and its trajectory in general is not of the Nambu-Goto type. For $|n|=1$ the single zero in general does not lie on Nambu-Goto type trajectory.