Chamseddine, Fr\"ohlich, Grandjean Metric and Localized Higgs Coupling on Noncommutative Geometry

TL;DR

This paper introduces a geometrized Higgs mechanism within noncommutative geometry, where Higgs couplings depend on local coordinates and are computed via Wilson loops in a specific gauge connection framework.

Contribution

It presents a novel approach to localize Higgs couplings using the gravitational sector in the Connes-Lott model, extending the geometric understanding of the Higgs mechanism.

Findings

Higgs-like couplings depend on local coordinates in spacetime.

Localized couplings are computed through Wilson loops of gauge fields.

The approach integrates noncommutative geometry with gauge theory for the standard model.

Abstract

We propose a geometrized Higgs mechanism based on the gravitational sector in the Connes-Lott formulation of the standard model, which has been constructed by Chamseddine, Fr$\ddot{o}$hlic and Grandjean. The point of our idea is that Higgs-like couplings depend on the local coordinates of the four-dimensional continuum,$M_4$. The localized couplings can be calculated by the Wilson loops of the $U(1)_{EM}$ gauge field and the connection, which is defined on $Z_2\times{M_4}$.