Warped Kaluza-Klein Towers Revisited

TL;DR

This paper revisits warped Kaluza-Klein models without metric singularities, analyzing scalar field propagation, boundary conditions, and mass spectra, including tachyons, with numerical examples illustrating physical implications.

Contribution

It provides a rigorous mathematical formulation of boundary conditions and mass spectra in a smooth warped extra dimension model, extending previous singular models.

Findings

Derived boundary conditions ensuring hermiticity of the scalar field operator

Computed mass eigenvalue towers and identified tachyonic states

Numerical examples illustrating mass spectra and probability densities

Abstract

Inspired by the warped Randall Sundrum scenario proposed to solve the mass scale hierarchy problem with a compactified fifth extra dimension, a similar model with no metric singularities has been elaborated. In this framework, the Kaluza-Klein reduction equations for a real massless scalar field propagating in the bulk have been studied carefully from the point of view of hermiticity so as to formulate in a mathematically rigorous way all the possible boundary conditions and corresponding mass eigenvalue towers and tachyon states. The physical masses as observable in our four-dimensional brane are deduced from these mass eigenvalues depending on the location of the brane on the extra dimension axis. Examples of mass towers and tachyons and related field probability densities are presented from numerical computations performed for some arbitrary choices of the parameters of the model.