Resonant excitations of the 't Hooft-Polyakov monopole

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 $t^{-5/6}$.

Comments: 4 pages