Vortons with Abelian and non-Abelian currents and their stability

Gianni Tallarita,Peter Bedford,Adam Peterson,Stefano Bolognesi

doi:10.1140/epjc/s10052-019-7540-7

Abstract

We explore vorton solutions in the Witten’s U(1) times U(1) model for cosmic strings and in a modified version U(1) times SO(3) obtained by introducing a triplet of non-Abelian fields to condense inside the string. We restrict to the case in which the unbroken symmetry in the bulk remains global. The vorton solutions are found numerically for certain choices of parameters and compared with an analytical solutions obtained in the thin vorton limit. We also discuss the vorton decay into Q-rings (or spinning Q-balls) and, to some extent, the time dependent behavior of vortons above the charge threshold.

Highlights

For the particular model we consider, vorton solutions can be constructed from solutions in the original U (1) × U (1) model by mapping the global U (1) to a subgroup of S O(3) and the S1 internal moduli space to a S1 ⊂ S2 at a certain latitude of the sphere
In this paper we studied vorton solution in an Abelian model, which is a global version of the Witten superconducting string model, and a non-Abelian generalization where a triplet of fields transforming under S O(3) condenses in the core of the vortex
We discovered an instability channel of vorton solutions for ω > ωcrit, explicitly showing their decay into Q-ring solutions

Summary

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For numerically constructing solutions it is easiest to recast the form of the ansatz to simplify the form of the equations of motion. With this form of the ansatz we find the equations to solve: We will solve this system using a relaxation procedure following from the energy minimization condition. We have chosen the numerical values for the constants such that vortices within the model develop non-zero profiles for the χi field in their cores. Note that the solutions to (14) are the same as in the Witten model (1) when the non-Abelian field χ is chosen to be constrained to, for example, the internal i = {1, 2} plane χ 3 = 0. We will discuss numerical solutions of the equations (19) with boundary conditions (20), (21), and (22) as well as solutions to the Abelian case (11) in Sect. Before discussing numerical solutions we wish to present some analytical results in some interesting physical limits

Thin vorton limit

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Numerical solutions and results

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Conclusion

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