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 ${\pi }_0(H)$. In particular, we find that, unless $2{\sin }^2{\theta }_W$ is a rational number, the thermal splitting of electroweak Z-strings by magnetically neutral black holes is impossible, even though ${\pi }_0(H)$ is trivial.

12 pages revtex -- Published version (some points clarified)

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