Stability of Scalar Fields in Warped Extra Dimensions

TL;DR

This paper develops a comprehensive theoretical framework to analyze the stability of models with warped extra dimensions involving multiple scalar fields, deriving conditions for stability and zero modes, and providing explicit stable and unstable examples.

Contribution

It introduces a general method to study scalar perturbations in warped extra dimension models, including criteria for zero modes and stability, applicable to brane and bulk scalar configurations.

Findings

Models without branes are free of tachyonic modes.

Certain scalar configurations with specific parity are perturbatively stable.

An explicit example stabilizes a compact extra dimension without branes.

Abstract

This work sets up a general theoretical framework to study stability of models with a warped extra dimension where N scalar fields couple minimally to gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk scalars, and general domain-wall models. We derive the Schrodinger equation governing the spin-0 spectrum of perturbations of such a system. This result is specialized to potentials generated using fake supergravity, and we show that models without branes are free of tachyonic modes. Turning to the existence of zero modes, we prove a criterion which relates the number of normalizable zero modes to the parities of the scalar fields. Constructions with definite parity and only odd scalars are shown to be free of zero modes and are hence perturbatively stable. We give two explicit examples of domain-wall models with a soft wall, one which admits a zero mode and one which does not. The latter is an example of a model that stabilizes a compact extra dimension using only bulk scalars and does not require dynamical branes.