The Einstein-Hilbert-Yang-Mills-Higgs Action and the Dirac-Yukawa Operator

TL;DR

This paper demonstrates how the standard model's full action functional can be geometrically derived using generalized Dirac operators, unifying gravity, gauge theories, and the Higgs sector within a single framework.

Contribution

It introduces a new geometrical model building approach that unifies Einstein gravity, Yang-Mills theories, and the Higgs mechanism through generalized Dirac operators.

Findings

Unified geometric description of gravity and gauge theories.

Higgs field related to gravitational potential.

Model parameters satisfy relations similar to Connes-Lott approach.

Abstract

In this article we show in some detail how the full action functional of the standard model of elementary particle physics can be described within the geometrical setting of generalized Dirac operators. We thereby introduce a new model building kit for (a certain class of) gauge invariant theories which provides a unified geometrical description of Einstein's theory of gravity and Yang-Mills gauge theories on the "classical" level. Moreover, when the gauge symmetry is spontaneously broken, the Higgs sector as well has a natural geometrical interpretation. It turns out that the Higgs field is related to the gravitational potential. Since the full action functional of the standard model is derived in one stroke, the appropriate parameters of the model have to satisfy certain relations similar to those in the Connes-Lott approach. Likewise, this may yield some phenomenological consequences, which is illustrated by using the gauge group of the standard model in the case of $N-$generations of leptons and quarks.