Stability of Superconducting Strings

TL;DR

This paper examines the stability of superconducting strings and vortons through classical simulations and quantum analysis, revealing conditions for their stability and decay mechanisms, with implications for cosmic string models.

Contribution

It introduces a combined classical and quantum framework for analyzing superconducting string stability, including a new world-sheet formalism for decay rates and insights into zero-mode dynamics.

Findings

Superconducting strings relax to stable vorton configurations via Nambu-Goldstone boson radiation.

Maximum zero-mode energy exceeds fermion mass, contrary to previous assumptions.

Decay rates of zero modes are suppressed by string curvature and non-adiabatic effects.

Abstract

We investigate the stability of superconducting strings as bound states of strings and fermion zero modes at both the classical and quantum levels. The dynamics of these superconducting strings can result in a stable configuration, known as a vorton. We mainly focus on global strings, but the majority of the discussion can be applied to local strings. Using lattice simulations, we study the classical dynamics of superconducting strings and confirm that they relax to the vorton configuration through Nambu-Goldstone boson radiation, with no evidence of over-shooting that would destabilize the vorton. We explore the tunneling of fermion zero modes out of the strings. Both our classical analysis and quantum calculations yield consistent results: the maximum energy of the zero mode significantly exceeds the fermion mass, in contrast to previous literature. Additionally, we introduce a world-sheet formalism to evaluate the decay rate of zero modes into other particles, which constitute the dominant decay channel. We also identify additional processes that trigger zero-mode decay due to non-adiabatic changes of the string configuration. In these decay processes, the rates are suppressed by the curvature of string loops, with exponential suppression for large masses of the final states. We further study the scattering with light charged particles surrounding the string core produced by the zero-mode current and find that a wide zero-mode wavefunction can enhance vorton stability.