Orbifold family unification using vectorlike representation on six dimensions

TL;DR

This paper explores orbifold family unification in six-dimensional space-time using vectorlike fermion representations, leading to models with three families of standard model matter and analyzing flavor number relationships.

Contribution

It introduces a novel approach using vectorlike representations in six-dimensional orbifold models to achieve three-family unification without non-Abelian flavor symmetries.

Findings

Models with three or more neutrino singlets are constructed.

No non-Abelian continuous flavor gauge symmetries are present in these models.

Relationships between flavor numbers from different fermion representations are clarified.

Abstract

In orbifold family unification on the basis of $SU(N)$ gauge theory on the six-dimensional space-time $M^4\times T^2/Z_m$ ($m=2, 3, 4, 6$), enormous numbers of models with three families of the standard model matter multiplets are derived from a massless Dirac fermion with a vectorlike representation $[N, 3] + [N, N-3]$ of $SU(N)$ ($N = 8, 9$). They contain models with three or more than three neutrino singlets and without any non-Abelian continuous flavor gauge symmetries. The relationship between flavor numbers from a fermion with $[N, N-k]$ and those from a fermion with $[N, k]$ are studied from the viewpoint of charge conjugation.