Metastable Kinks in the Orbifold

TL;DR

This paper analyzes the stability of static bulk scalar field configurations in extra-dimensional orbifold models, identifying conditions under which these configurations are stable or unstable, with implications for model building.

Contribution

It provides a detailed Sturm-Liouville stability analysis and a general criterion for determining the stability of nodeless scalar field configurations in orbifold models.

Findings

All but the lowest-lying configurations are unstable.

A general stability criterion for nodeless solutions is established.

Most static configurations in the model are shown to be unstable.

Abstract

We consider static configurations of bulk scalar fields in extra dimensional models in which the fifth dimension is an $S^1/Z_2$ orbifold. There may exist a finite number of such configurations, with total number depending on the size of the orbifold interval. We perform a detailed Sturm-Liouville stability analysis that demonstrates that all but the lowest-lying configurations - those with no nodes in the interval - are unstable. We also present a powerful general criterion with which to determine which of these nodeless solutions are stable. The detailed analysis underlying the results presented in this letter, and applications to specific models, are presented in a comprehensive companion paper.