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.
Highlights
One of the most intriguing riddles in particle physics is the origin of family replication in standard model (SM) matter multiplets
In Ref. [23], we find that the number of neutrino singlets is less than 3, the smallest gauge group is SUð9Þ, and most models contain an extra non-Abelian continuous gauge group relating to a flavor symmetry, under the precondition that three SM families are derived from a massless Dirac fermion in a chiral representation 1⁄2N; k of SUðNÞ
We have studied the possibility of family unification on the basis of SUðNÞ gauge theory in the six-dimensional space-time M4 × T2=Zm (m 1⁄4 2, 3, 4, 6)
Summary
One of the most intriguing riddles in particle physics is the origin of family replication in standard model (SM) matter multiplets. [23], we find that the number of neutrino singlets is less than 3, the smallest gauge group is SUð9Þ, and most models contain an extra non-Abelian continuous gauge group relating to a flavor symmetry, under the precondition that three SM families are derived from a massless Dirac fermion in a chiral representation 1⁄2N; k of SUðNÞ. SM families are derived from a massless Dirac fermion in a vectorlike representation 1⁄2N; k þ 1⁄2N; N − k of SUðNÞ, there is a possibility that some models possess features such that the number of neutrino singlets is 3 or more than 3, the smallest gauge group is less than SUð9Þ, and all extra gauge symmetries are Abelian. We explain the orbifold T2=Zm (m 1⁄4 2, 3, 4, 6), a sixdimensional fermion and a decomposition of field in 1⁄2N; k
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