Family Unification from Universality

TL;DR

The paper explores how universality groups related to fermion families can be used to develop grand family unification models, proposing a preonic structure that avoids hierarchy and anomaly issues.

Contribution

It introduces a framework using universality groups to construct grand family unification models with a preonic fermion structure.

Findings

Identifies weak and strong universality groups for unification.

Shows decomposition of SU(8N) into family structures.

Proposes a preonic model avoiding hierarchy problems.

Abstract

A direct consequence of the occurrence of fermion families is the invariance of currents under certain groups of (universality) transformations. We show how these universality groups can themselves be used to find and study grand family unification models. Identifying two independent - weak and strong - universality groups and assuming that the grand unification group is SU(8N), its subgroup respecting either weak or strong universality is shown to be G = SU(2)xU(1)xSU(3). The fundamental representation of SU(8N) decomposes as N families of leptons and quarks. In the G-invariant limit, all fermions are left-handed. A mechanism for generating the correct number of right-handed fermions with the correct couplings so as to give pure vector colour and electromagnetic currents is exhibited. Universality is shown to result most naturally from a preonic structure of fermions. In such a preonic picture there are no ultraheavy gauge bosons and no anomaly or hierarchy problem.