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, $E_n={\omega }_n-i{\gamma }_n$, 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 breatherlike excitation with an amplitude decaying at late times as $t^{-5/6}$.

Figure 1

The scattering cross section $\sigma (\omega )$.

Figure 2

The complex solutions of Eqs. (5, 6) for $n=3$.

Figure 3

The profile of $w(t,1)$ in Eq. (16) corresponding to the initial steplike perturbation, $\delta W(r)=\theta (1-r)$.