Towards unity of families: anti-SU(7) from Z(12-I) orbifold compactification

TL;DR

This paper proposes anti-SU(N) grand unification models to explain the origin of three fermion families, using orbifold compactification to realize the models and mechanisms for symmetry breaking.

Contribution

It introduces anti-SU(N) GUT models for family unification and demonstrates a specific Z(12-I) orbifold compactification example with the missing partner mechanism.

Findings

Minimal anti-SU(7) GUT model constructed.

Explicit orbifold compactification example provided.

Missing partner mechanism successfully realized.

Abstract

The problem of families, "Why are there three families of fermions?", is a long awaited question to be answered within a reasonable framework. We propose anti-SU($N$) groups for the unification of families in grand unification (GUT) groups, where the separation of color and weak gauge groups in the GUT is achieved by antisymmetric tensor Brout-Englert-Higgs boson instead of an adjoint representation. Theories of anti-SU($N$)'s are proposed for the unification of families. The minimal model is found as \antiSD \, GUT with the fermion representation [3]+2[2]+8[\bar-1]. We present an example in a Z(12-I) orbifold compactification, where the missing partner mechanism is also realized.