Geometrization of the electro-weak model bosonic component

TL;DR

This paper develops a geometrical unification of gravity and the electro-weak model using a Kaluza-Klein framework, deriving Einstein-Yang-Mills action and explaining fermion doublets and symmetry breaking.

Contribution

It introduces a novel geometrical approach to unify gravity and electro-weak interactions via specific higher-dimensional manifolds and incorporates a Higgs field with opposite hypercharges.

Findings

Derivation of Einstein-Yang-Mills action from curvature reduction

Representation of fermion doublets within specific manifolds

Introduction of a Higgs field with opposite hypercharges

Abstract

In this work we develop a geometrical unification theory for gravity and the electro-weak model in a Kaluza-Klein approach; in particular, from the curvature dimensional reduction Einstein-Yang-Mills action is obtained. We consider two possible space-time manifolds: 1)$V^{4}\otimes S^{1}\otimes S^{2}$ where isospin doublets are identified with spinors; 2) $V^{4}\otimes S^{1}\otimes S^{3}$ in which both quarks and leptons doublets can be recast into the same spinor, such that the equal number of quark generations and leptonic families is explained. Finally a self-interacting complex scalar field is introduced to reproduce the spontaneous symmetry breaking mechanism; in this respect, at the end we get an Higgs fields whose two components have got opposite hypercharges.