Radial excitations of current-carrying vortices

Betti Hartmann,Florent Michel,Patrick Peter

doi:10.1016/j.physletb.2017.02.015

Abstract

We report on the existence of a new type of cosmic string solutions in the Witten model with U(1)×U(1) symmetry. These solutions are superconducting with radially excited condensates that exist for both gauged and ungauged currents. Our results suggest that these new configurations can be macroscopically stable, but microscopically unstable to radial perturbations. Nevertheless, they might have important consequences for the network evolution and particle emission. We discuss these effects and their possible signatures. We also comment on analogies with non-relativistic condensed matter systems where these solutions may be observable.

Highlights

IntroductionE.g., vortex lines in condensed matter physics [1,2], superfluid vortices (see e.g. [3]), non-Abelian vortices (see e.g. [4]), frequently appear as solutions of high energy field theories where they are called cosmic strings [5]; these include grand unified (GUT) or superstring theories
Linear topological defects, e.g., vortex lines in condensed matter physics [1,2], superfluid vortices, non-Abelian vortices, frequently appear as solutions of high energy field theories where they are called cosmic strings [5]; these include grand unified (GUT) or superstring theories
Our discussion here goes one step further by showing that there is a finite number of such bound states, each of which leading to an instability in the current condensate, an instability that will be tamed by the nonlinear terms: one expects that for each value of w, the full nonlinear set of equations should lead to a series of solutions with finite energy per unit length and tension in the form of a ground state and excited modes

Summary

Introduction

E.g., vortex lines in condensed matter physics [1,2], superfluid vortices (see e.g. [3]), non-Abelian vortices (see e.g. [4]), frequently appear as solutions of high energy field theories where they are called cosmic strings [5]; these include grand unified (GUT) or superstring theories. Higgs model with a Mexican hat potential, there are no known analytical solutions, straight and static ones [9] having only been constructed numerically These so-called Abelian–Higgs or Abrikosov–Nielsen–Olesen (ANO) vortices have a localized energymomentum tensor and a quantized magnetic-like flux with the magnetic-like field pointing in the direction of the string axis. Currents up to 1020 Amps (GUT case) can be induced by either bosonic or fermionic [22] charge carriers In the former case, the scalar field that undergoes spontaneous symmetry breaking, leading to the formation of the strings, couples non-trivially to a second one. They are important to understand the mathematical structure of the theory, and may have nontrivial consequences for the evolution of the string network as well as the emission of particles during reconnection between two strings

The model

Small condensates the gauge covariant derivatives read

Numerical results

Discussion