Stability of gravity-scalar systems for domain-wall models with a soft wall

TL;DR

This paper demonstrates that stable, brane-free soft-wall models with a compact extra dimension can be constructed using bulk scalar fields, ensuring stability and addressing the hierarchy problem within a gravity-scalar framework.

Contribution

It introduces a method to create stable RS soft-wall models without fundamental branes using the superpotential approach, ensuring stability against tachyonic and zero modes.

Findings

Configurations are free of tachyonic modes.

Models are free of zero modes with odd scalar parity.

Applicable to AdS/QCD correspondence.

Abstract

We show that it is possible to create an RS soft-wall model, a model with a compact extra dimension, without using fundamental branes. All that is required are bulk scalar fields minimally coupled to gravity. Of crucial importance is the stability of the size of the extra dimension. Without branes, one cannot easily implement the Goldberger-Wise mechanism, and instead it must be shown that the scalar configuration is stable in its own right. We use the superpotential approach for generating solutions, the so called 'fake supergravity' scenario, and show that configurations generated in such a way are always free of tachyonic modes. Furthermore, we show that the model is also free of zero modes (in the spin-0 sector) if all the scalars have odd parity. We discuss the hierarchy problem in soft-wall models, and applications of our analysis to the AdS/QCD correspondence.