Krajewski diagrams and the Standard Model

TL;DR

This paper catalogs all Krajewski diagrams representing the Standard Model within noncommutative geometry, providing a foundation for constructing beyond-Standard Model theories by addressing spectral triple limitations.

Contribution

It offers a complete list of Krajewski diagrams for the Standard Model and discusses how to extend these models to include new particles beyond the Standard Model.

Findings

List of all Krajewski diagrams for the Standard Model

Identification of spectral triple limitations related to Poincare duality

Framework for extending models with additional particles

Abstract

This paper provides a complete list of Krajewski diagrams representing the standard model of particle physics. We will give the possible representations of the algebra and the anomaly free lifts which provide the representation of the standard model gauge group on the fermionic Hilbert space. The algebra representations following from the Krajewski diagrams are not complete in the sense that the corresponding spectral triples do not necessarily obey to the axiom of Poincare duality. This defect may be repaired by adding new particles to the model, i.e. by building models beyond the standard model. The aim of this list of finite spectral triples (up to Poincare duality) is therefore to provide a basis for model building beyond the standard model.