Expansion in the Width: the Case of Vortices

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 $n\ge 2$ 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.

25 pages, LaTeX, no figures

References in corpus (2)

• On dynamics of cylindrical and spherical relativistic domain walls of finite thickness
• On expansion in the width for domain walls

Cited by in corpus (11)

• Loop decay in Abelian-Higgs string networks
• Multi-messenger constraints on Abelian-Higgs cosmic string networks
• The Rise and Fall of the Cosmic String Theory for Cosmological Perturbations
• Cosmological evolution of cosmic strings with time-dependent tension
• Revised bounds on local cosmic strings from NANOGrav observations
• Expansion in the Width and Collective Dynamics of a Domain Wall
• Gauge string in the fermion asymmetric matter
• Non-Abelian Vortex-String Dynamics from Nonlinear Realization
• Integrability in Theories with Local U(1) Gauge Symmetry
• Dissipative Dynamics of Solitons in Planar Ferromagnets
• Radial kinks in a Schwarzschild-like geometry