Selection rules for splitting strings

TL;DR

This paper investigates how embedding the abelian Higgs model in larger theories introduces new selection rules for string splitting, especially affecting electroweak Z-string decay via black holes, based on charge quantization conditions.

Contribution

It reveals that charge quantization conditions can impose additional constraints on string decay processes, beyond topological considerations, especially in the electroweak context.

Findings

Charge quantization conditions can prevent string splitting in certain models.

Electroweak Z-string splitting by black holes depends on the rationality of 2sin^2θ_W.

Topology change criteria complement traditional topological invariants.

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.