On a Classification of Irreducible Almost-Commutative Geometries V

TL;DR

This paper extends the classification of irreducible almost-commutative geometries with non-degenerate spectral action to more complex internal algebras, identifying four main particle physics models including extensions of the standard model.

Contribution

It introduces a classification for geometries with six simple summands and identifies four novel particle models within this framework.

Findings

Identified four main particle models from the extended classification.

Extended the classification to internal algebras with six simple summands.

Found models including standard model extensions and electro-strong variants.

Abstract

We extend a classification of irreducible, almost-commutative geometries whose spectral action is dynamically non-degenerate, to internal algebras that have six simple summands. We find essentially four particle models: An extension of the standard model by a new species of fermions with vectorlike coupling to the gauge group and gauge invariant masses, two versions of the electro-strong model and a variety of the electro-strong model with Higgs mechanism.