Abstract
Stable ring solutions supported by the angular momentum caused by superconducting charge and current have been suggested to exist in the gauged U(1)×U(1) field theory. We construct potentially cosmologically relevant solutions using gradient flow for the first time and present the strongest evidence to date that they are stable to axial and, crucially, nonaxial perturbations. More importantly, we illustrate quantitative agreement with semianalytic predictions based on the thin string approximation, which validates world sheet action approaches to their formation and evolution.
Highlights
Introduction.—Cosmic strings will be formed in a cosmological phase transition where the vacuum manifold can support noncontractible loops
It was suggested by Witten [2] that they could act as superconducting wires with interesting consequences. He illustrated this point using a gauged Uð1Þ × Uð1Þ bosonic field theory, [3] but for our purposes it will be sufficient to consider the neutral limit [4], where only the vortex field φ is gauged with Lagrangian density where Dμ 1⁄4 ∂μ − igAμ, and Fμν 1⁄4 ∂μAν − ∂νAμ
While this work shows that solutions similar to vortons can exist, they are not cosmologically relevant, since their size is very small and, length scales associated with the fields are on the order of the size of the overall defect [22]. In contrast, vortons of cosmological importance should be expected to have radii that are many orders of magnitude larger than the core width. (iv) Kinky vortons [25]—a 2D analog of vortons— have been constructed, aided by an exact analytic solution for the superconducting domain wall solution, and their stability was confirmed using numerical and analytic techniques based on the thin string approximation (TSA) [26]
Summary
Introduction.—Cosmic strings will be formed in a cosmological phase transition where the vacuum manifold can support noncontractible loops. It is possible [16,17,18] to investigate the stability of these ring solutions to transverse and longitudinal perturbations by supplementing the Nambu action with fields representing the charge and current on the world sheet—“world sheet action approaches.” In particular, one can investigate the impact of small perturbations to the position of the string ∝ exp1⁄2iðΩmt − mθÞ, where the Ωm 1⁄4 2πfm is predicted and will be tested in what follows.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
