Einstein-Yang-Mills-Dirac systems from the discretized Kaluza-Klein theory

TL;DR

This paper develops a unified framework combining gravity and non-Abelian gauge interactions using a discretized Kaluza-Klein approach, revealing natural couplings and encompassing existing gravity-gauge models.

Contribution

It introduces a novel discretized Kaluza-Klein model with a modified Dirac operator, unifying gauge interactions with gravity and deriving known models as special cases.

Findings

Couplings of chiral spinors to gauge fields emerge naturally.

Gravity-QCD-quark and gravity-electroweak-quark-lepton models are special cases.

The framework incorporates new interactions through a modified Dirac operator.

Abstract

A unified theory of the non-Abelian gauge interactions with gravity in the framework of a discretized Kaluaza-Kleine theory is constructed with a modified Dirac operator and wedge product. All the couplings of chiral spinors to the non-Abelian gauge fields emerge naturally as components of the couplings of the chiral spinors to the generalized gravity together with some new interactions. In particular, the currently prevalent gravity-QCD-quark and gravity-electroweak-quark-lepton models are shown to follow as special cases of the general framework.