Teleparallel Equivalent of Non-Abelian Kaluza-Klein Theory

TL;DR

This paper develops a teleparallel non-abelian Kaluza-Klein theory that unifies gravity and gauge fields within a four-dimensional spacetime, featuring a natural Planck-scale length for the fiber space.

Contribution

It introduces a teleparallel framework for non-abelian Kaluza-Klein theory, maintaining four-dimensional spacetime and defining a natural compactification scale.

Findings

Fiber space is higher-dimensional, spacetime remains four-dimensional.

The model unifies gravitational and gauge fields in a gauge theory.

The compactification scale is of the order of the Planck length.

Abstract

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher-dimensional, spacetime being kept always four-dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast to the ordinary Kaluza-Klein models, this theory defines a natural length-scale for the compact sub-manifold of the fiber space, which is shown to be of the order of the Planck length.