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.

arXiv comment24 pages

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• Tetrahedral Symmetry A${}_4$ in Anti-SU(5) GUT
• Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models
• Grand unfication models from SO(32) heterotic string
• Jarlskog determinant and data on flavor matrices