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arXiv · 0708.4008

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

Manuel Toharia·Mark Trodden
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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.

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Manuel Toharia, Mark Trodden. 2007-09-25. Existence and Stability of Non-Trivial Scalar Field Configurations in Orbifolded Extra Dimensions. https://doi.org/10.1103/physrevd.77.025029

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