Existence and Stability of Non-Trivial Scalar Field Configurations in Orbifolded Extra Dimensions

TL;DR

This paper investigates the existence and stability of scalar field configurations in five-dimensional orbifolded spacetimes, identifying conditions for stable nodeless solutions and analyzing their dependence on the potential and orbifold size.

Contribution

It provides a general stability criterion for nodeless scalar field solutions in orbifolded extra dimensions, extending understanding of their stability properties.

Findings

Nodeless solutions can be stable depending on the potential.

Configurations with nodes are generally unstable.

A general criterion for stability of nodeless solutions is established.

Abstract

We consider the existence and stability of static configurations of a scalar field in a five dimensional spacetime in which the extra spatial dimension is compactified on an $S^1/Z_2$ orbifold. For a wide class of potentials with multiple minima there exist a finite number of such configurations, with total number depending on the size of the orbifold interval. However, a Sturm-Liouville stability analysis demonstrates that all such configurations with nodes in the interval are unstable. Nodeless static solutions, of which there may be more than one for a given potential, are far more interesting, and we present and prove a powerful general criterion that allows a simple determination of which of these nodeless solutions are stable. We demonstrate our general results by specializing to a number of specific examples, one of which may be analyzed entirely analytically.