Almost-Commutative Geometries Beyond the Standard Model

TL;DR

This paper presents a counterexample in almost-commutative geometries that extends the standard model of particle physics with new fermions, offering a potential dark matter candidate and challenging previous conjectures about these geometries.

Contribution

It provides the first known extension of the standard model within noncommutative geometry that includes new fermions, suggesting possible experimental compatibility and dark matter implications.

Findings

Introduction of a new Yang-Mills-Higgs model with additional fermions.

Potential dark matter candidate through composite particles.

Challenges previous conjectures limiting geometries to the standard model.

Abstract

In [7-9] and [10] the conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this publication a counter example will be given. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model of particle physics and two new fermions of opposite electro-magnetic charge. This is the second Yang-Mills-Higgs model within noncommutative geometry, after the standard model, which could be compatible with experiments. Combined to a hydrogen-like composite particle these new particles provide a novel dark matter candidate.