Dyon-fermion dynamics

We continue our study of the effect of light fermions on the charge degree of freedom of magnetic monopoles. Even though the gauge coupling is weak, the Fermi vacuum is strongly perturbed by its coupling to the charge degree of freedom of the monopole. To obtain a correct picture of the vacuum we concentrate on the lowest partial wave of the Fermi field about the monopole core. We find that this simplified system can be transformed to an equivalent one-dimensional scalar field theory in which the original fermions appear as sine-Gordon solitons and the monopole charge is determined by the expectation value of the scalar field at spatial infinity. The scalar theory, though not soluble, is sufficiently transparent for us to extract the qualitative physics of monopole charge in the presence of light fermions: the Witten formula for the dependence of monopole charge on vacuum angle, ${Q}_{n}=e(n\ensuremath{-}\frac{\ensuremath{\theta}}{2\ensuremath{\pi}})$, is true no matter how small the Fermi mass $m$; the fractional charge is spread through the Fermi vacuum over a region size ${m}^{\ensuremath{-}1}$ and the excitation energy of a charged state is of order $m$; the existence of vacuum structure on such a small energy scale means that certain exotic fermion-monopole scattering processes have very large cross sections. In particular it appears that in grand unification theories monopoles will catalyze baryon decay at typical strong-interaction rates.