A Classical Analogue to the Standard Model, Chapter 2: Colour interactions and fermions from scalar fields on $\mathbb{C}^{\wedge 6}$

TL;DR

This paper explores a mathematical model using complex manifolds to replicate key features of the Standard Model, including color charge and fermion properties, offering a new framework for studying confinement.

Contribution

It introduces a novel complex manifold-based model that supports fermions with Standard Model-like properties and demonstrates the emergence of SU(3) color charge in higher dimensions.

Findings

Fermions acquire SU(3) color charge on increasing manifold dimension

Model supports fermions with Standard Model-like spin and dimensions

Provides a new environment to study color confinement

Abstract

This paper continues the study of quasiparticles on complex manifolds with anticommuting co-ordinates, and shows that on increasing the dimensionality of the complex manifold from $\mathbb{C}^{\wedge 2}$ to $\mathbb{C}^{\wedge 6}$, the dimension-$L^{-1/2}$ spinor excitations in the associated effective field theory on $\mathbb{R}^{1,3}$ acquire an $\mathrm{SU}(3)$ colour charge and assemble into composite spinors of dimension $L^{-3/2}$. This model provides a novel environment in which to study colour confinement, while also demonstrating the ability of the first member of the $\mathbb{C}^{\wedge 6\mathfrak{n}}$ series to support fermions having spin and dimensions consistent with the Standard Model.