Elementary Kaluza-Klein Towers revisited

TL;DR

This paper reexamines the Kaluza-Klein mass spectrum for scalar fields in a five-dimensional scenario, revealing new boundary conditions and mass towers, and discusses potential implications for fundamental constants and symmetry breaking.

Contribution

It introduces new physically allowed boundary conditions leading to novel mass spectra, including irregular towers and tachyons, in the Kaluza-Klein framework.

Findings

Discovery of new boundary conditions for scalar fields

Identification of non-regular mass towers and tachyons

Discussion of possible variation of the speed of light in extra dimensions

Abstract

Considering that the momentum squared in the extra dimensions is the physically relevant quantity for the generation of the Kaluza-Klein mass states, we have reanalyzed mathematically the procedure for five dimensional scalar fields within the Arkhani-Ahmed, Dimopoulos and Dvali scenario. We find new sets of physically allowed boundary conditions. Beside the usual results, they lead to new towers with non regular mass spacing, to lonely mass states and to tachyons. We remark that, since the SO(1,4) symmetry is to be broken due to the compactification of the extra dimensions, the speed of light could be different in the fifth dimension. This would lead to the possible appearance of a new universal constant besides $\hbar$ and $c$.