Resonant excitations of the 't Hooft-Polyakov monopole

TL;DR

This paper demonstrates that the 't Hooft-Polyakov monopole has an infinite spectrum of resonant modes that influence its response to perturbations, leading to long-lived breather-like excitations with specific decay properties.

Contribution

It reveals the existence of an infinite number of quasinormal modes in the monopole, detailing their properties and impact on monopole dynamics, which was previously unknown.

Findings

Infinite resonant modes with complex eigenvalues

Frequencies approach the vector boson mass for large mode number

Long-lived breather-like excitations with specific decay behavior

Abstract

The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, $E_n=\omega_n-i\gamma_n$, satisfying the outgoing radiation condition. For $n\to\infty$, their frequencies $\omega_n$ approach the mass of the vector boson, $M_W$, while their lifetimes $1/\gamma_n$ tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breather-like excitation characterized by pulsations with a frequency approaching $M_W$ and with an amplitude decaying at late times as $t^{-5/6}$.