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

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.