Survival of scalar zero modes in warped extra dimensions

TL;DR

This paper analyzes the stability of scalar zero modes in warped extra-dimensional models with gravity, showing that certain models retain zero modes despite warping, which impacts their physical viability.

Contribution

It provides a formal solution to coupled Schrödinger equations for scalar perturbations in warped extra dimensions, revealing the persistence of zero modes in specific models.

Findings

Normalisable zero modes can survive in warped models with two scalars.

Presence of zero modes indicates potential instability in certain models.

Method to determine zero mode existence via eigenvalues of a solution matrix.

Abstract

Models with an extra dimension generally contain background scalar fields in a non-trivial configuration, whose stability must be ensured. With gravity present, the extra dimension is warped by the scalars, and the spin-0 degrees of freedom in the metric mix with the scalar perturbations. Where possible, we formally solve the coupled Schrodinger equations for the zero modes of these spin-0 perturbations. When specialising to the case of two scalars with a potential generated by a superpotential, we are able to fully solve the system. We show how these zero modes can be used to construct a solution matrix, whose eigenvalues tell whether a normalisable zero mode exists, and how many negative mass modes exist. These facts are crucial in determining stability of the corresponding background configuration. We provide examples of the general analysis for domain-wall models of an infinite extra dimension and domain-wall soft-wall models. For 5D models with two scalars constructed using a superpotential, we show that a normalisable zero mode survives, even in the presence of warped gravity. Such models, which are widely used in the literature, are therefore phenomenologically unacceptable.