Kaluza-Klein towers for real vector fields in flat space

TL;DR

This paper analyzes the spectrum of real vector fields in five-dimensional flat space with compactified extra dimensions, deriving boundary conditions and resulting Kaluza-Klein mass towers with vector and scalar states.

Contribution

It systematically derives all allowed boundary conditions and computes the resulting Kaluza-Klein mass spectra for vector fields in flat extra dimensions.

Findings

Mass towers depend on bulk mass and boundary parameters

Boundary conditions determine the presence of scalar states

Explicit spectra for different compactification scenarios

Abstract

We consider a free real vector field propagating in a five dimensional flat space with its fifth dimension compactified either on a strip or on a circle and perform a Kalaza Klein reduction which breaks SO(4,1) invariance while reserving SO(3,1) invariance. Taking into account the Lorenz gauge condition, we obtain from the most general hermiticity conditions for the relevant operators all the allowed boundary conditions which have to be imposed on the fields in the extra-dimension. The physical Kaluza-Klein mass towers, which result in a four-dimensional brane, are determined in the different distinct allowed cases. They depend on the bulk mass, on the parameters of the boundary conditions and on the extra parameter present in the Lagrangian. In general, they involve vector states together with accompanying scalar states.