Kaluza-Klein towers for spinors in flat space

TL;DR

This paper analyzes the generation of four-dimensional Kaluza-Klein spinor mass towers from a five-dimensional flat space with compactified extra dimension, considering boundary conditions and symmetries.

Contribution

It provides a comprehensive analysis of boundary conditions and symmetry considerations for Kaluza-Klein spinor towers in flat five-dimensional space.

Findings

Allowed boundary conditions for spinors are classified.

General equations for mass towers are derived.

Numerical examples illustrate the mass spectrum.

Abstract

Considering a massive or massless free spinor field propagating in a flat five dimensional space with its fifth dimension compactified either on a strip or on a circle, we analyse the procedure of generation of the four dimensional Kaluza-Klein spinor mass towers. Requiring the five dimensional Dirac operator to be symmetric, the set of all the allowed boundary conditions is obtained. In the determination of the boundary conditions and in the Kaluza-Klein reduction equations, the SO(3,1) and parity invariances in the space-time subspace are carefully taken into account. The equations determining the mass towers are written in full generality. A few numerical examples are given.