Fermions in five-dimensional brane world models

TL;DR

This paper analyzes fermion fields in five-dimensional warped brane world models, focusing on the conditions for consistent Kaluza-Klein decomposition and implications for four-dimensional effective theories.

Contribution

It identifies which five-dimensional fermion Lagrangians allow consistent Kaluza-Klein decomposition and examines the case that best reproduces the Standard Model in Randall-Sundrum models.

Findings

Most five-dimensional fermion Lagrangians do not permit consistent Kaluza-Klein decomposition.

Certain Lagrangians lead to pathologies in the effective four-dimensional theory.

The case closest to the Standard Model is analyzed in detail within the Randall-Sundrum background.

Abstract

In the present paper the fermion fields, living in the background of five-dimensional warped brane world models with compact extra dimension, are thoroughly examined. The Kaluza-Klein decomposition and isolation of the physical degrees of freedom is performed for those five-dimensional fermion field Lagrangians, which admit such a decomposition to be performed in a mathematically consistent way and provide a physically reasonable four-dimensional effective theory. It is also shown that for the majority of five-dimensional fermion field Lagrangians there are no (at least rather obvious) ways to perform the Kaluza-Klein decomposition consistently. Moreover, in these cases one may expect the appearance of various pathologies in the four-dimensional effective theory. Among the cases, for which the Kaluza-Klein decomposition can be performed in a mathematically consistent way, the case, which reproduces the Standard Model by the zero Kaluza-Klein modes most closely regardless of the size of the extra dimension, is examined in detail in the background of the Randall-Sundrum model.