The Einstein-Yang-Mills equations from Bianchi identities

TL;DR

This paper introduces a new extension to the Kaluza-Klein framework that derives SU(n) Einstein-Yang-Mills theories by incorporating torsion in five-dimensional spacetime while keeping four-dimensional spacetime torsion-free.

Contribution

It presents a novel method to obtain Einstein-Yang-Mills theories from higher dimensions using torsion, expanding the Kaluza-Klein approach.

Findings

Successfully derives SU(n) Einstein-Yang-Mills theories from the extended scheme

Shows consistent incorporation of torsion in five dimensions

Maintains torsion-free condition in four-dimensional spacetime

Abstract

We suggest a novel extension to the Kaluza-Klein scheme that allows us to obtain consistently all SU(n) Einstein-Yang-Mills theories. This construction is based on allowing the five-dimensional spacetime to carry some non-vanishing torsion; however, the four-dimensional spacetime remains intrinsically torsion-free.