Selection Rules for Splitting Strings

Abstract

It has been pointed out that Nielsen-Olesen vortices may be able to decay by pair production of black holes. We show that when the Abelian-Higgs model is embedded in a larger theory, the additional fields may lead to selection rules for this process---even in the absence of fermions---due to the failure of a charge quantization condition. We show that when there is topology change, the criterion based on the charge quantization condition supplements the usual criterion based on ${\ensuremath{\pi}}_{0}(H)$. In particular, we find that unless $2{sin}^{2}{\ensuremath{\theta}}_{W}$ is a rational number, the thermal splitting of electroweak $Z$ strings by magnetically neutral black holes is impossible, even though ${\ensuremath{\pi}}_{0}(H)$ is trivial.