Finding the Standard Model of Particle Physics, A Combinatorial Problem

TL;DR

This paper introduces a combinatorial problem involving the enumeration of irreducible Krajewski diagrams, which are crucial for modeling the Standard Model of particle physics within finite noncommutative geometries.

Contribution

It formulates the problem of finding irreducible Krajewski diagrams as a combinatorial challenge, linking finite geometries to particle physics models.

Findings

Defined the problem of constructing irreducible Krajewski diagrams.

Connected the diagrams to the localization of the Standard Model.

Highlighted the role of diagrams in classifying Yang-Mills-Higgs models.

Abstract

We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constrains. The Krajewski diagrams play a central role in the description of finite noncommutative geometries. They allow to localise the standard model of particle physics within the set of all Yang-Mills-Higgs models.