Resonant Excitations of the ’t Hooft–Polyakov Monopole

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=ω_n-iγ_n, satisfying the outgoing radiation condition. For n→∞, their frequencies ω_n approach the mass of the vector boson, M_W, while their lifetimes 1/γ_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 breatherlike excitation with an amplitude decaying at late times as t^-5/6.