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

Understand

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.