Kaluza-Klein towers for spinors in warped spaces

TL;DR

This paper derives boundary conditions for five-dimensional spinor fields in warped spaces, analyzing the resulting Kaluza-Klein towers and their mass spectra, with implications for standard model fermions in extra-dimensional theories.

Contribution

It provides a comprehensive derivation of boundary conditions compatible with hermiticity in warped spaces, including metric singularities, and explores the resulting Kaluza-Klein mass spectra.

Findings

Lowest Kaluza-Klein masses can be very small and sensitive to parameters

Higher masses are larger and more regularly spaced

If a standard model fermion is the lowest mode, other modes are significantly heavier

Abstract

All the boundary conditions compatible with the reduction of a five dimensional spinor field of bulk mass $M$ in a compactified warped space to a four dimensional brane are derived from the hermiticity conditions of the relevant operator. The possible presence of metric singularities is taken into account. Examples of resulting Kaluza-Klein spinor towers are given for a representative set of values for the basic parameters of the model and of the parameters describing the allowed boundary conditions, within the hypothesis that there exists one-mass-scale-only, the Planck mass. In many cases, the lowest mass in the tower is small and very sensitive to the parameters while the other masses are much higher and become more regularly spaced. In these cases, if a basic fermion of the standard model (lepton or quark) happens to be the lowest mass of a Kaluza-Klein tower, the other masses would be much larger and weakly dependent on the fermion which defines the tower.