Peristaltic modes of a single vortex in the Abelian Higgs model

Abstract

Using the Abelian Higgs model, we study the radial excitations of single vortex and their propagation modes along the vortex line. We call such beyond-stringy modes peristaltic modes of single vortex. With the profile of the static vortex, we derive the vortex-induced potential, i.e., single-particle potential for the Higgs and the photon field fluctuations around the static vortex, and investigate the coherently propagating fluctuations which correspond to the vibration of the vortex. We derive, analyze, and numerically solve the field equations of the Higgs and the photon field fluctuations around the static vortex with various Ginzburg-Landau parameter $\ensuremath{\kappa}$ and topological charge $n$. Around the Bogomol'nyi-Prasad-Sommerfield value or critical coupling ${\ensuremath{\kappa}}^{2}=1/2$, there appears a significant correlation between the Higgs and the photon field fluctuations mediated by the static vortex. As a result, for ${\ensuremath{\kappa}}^{2}=1/2$, we find the characteristic new-type discrete pole of the peristaltic mode corresponding to the quasibound state of coherently fluctuating fields and the static vortex. We investigate its excitation energy, correlation energy of coherent fluctuations, spatial distributions, and the resulting magnetic flux behavior in detail. Our investigation covers not only usual type-II vortices with $n=1$ but also type-I and type-II vortices with $n\ensuremath{\in}Z$ for the application to various general systems where the vortexlike objects behave as the essential degrees of freedom.