Family symmetries with extra dimensions

Abstract

Possibly one of the most interesting unanswered questions posed by the Standard Model is an explanation for the existence of three light generations of matter. Perhaps the most conservative extension to the Standard Model to offer an explanation is to include a symmetry between the families. One of the most promising candidates for this symmetry is the discrete group A4, the symmetry group of the tetrahedron. Extra dimensions have long been considered to be included in a final “Theory Of Everything”. More recently research into String Theory has led to more interest in extra dimensional theories. The geometry of these extra dimensions has also been used to generate discrete symmetries which may be exploited as a family symmetry. Grand Unified Theories seek to unify electromagnetism, the weak and the strong forces into a single unified force at high energy. If we wish for such a unification then restrictions are placed upon any family symmetry we may use. We study models which seek to explain the large leptonic mixing angles together with the small quark mixing angles and large quark hierarchy by considering models which incorporate the use of extra dimensions together with Grand Unified and family symmetries.

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