In particle physics, family symmetries or horizontal symmetries are various discrete, global, or local symmetries between quark-lepton families or generations. While being conceptually useful, these symmetries are not yet finally confirmed. Some potentially relevant option considered in the literature may be associated with the local chiral SU(3)F family symmetry introduced in 1980 and further developed. 
The choice of the SU(3)F as the underlying family symmetry beyond the Standard Model appears related to the following issues: (i) It provides a natural explanation of the number three of observed quark-lepton families; (ii) Its local nature conforms with the other local symmetries of the Standard Model, such as the weak isospin symmetry SU(2)W or color symmetry SU(3)C; (iii) Its chiral nature, according to which both left-handed and right-handed fermions are proposed to be fundamental triplets of the SU(3)F symmetry, provides the hierarchical mass spectrum of quark-lepton families as a result of a spontaneous symmetry breaking; (iv) It admits a natural unification with conventional Grand unified theories (GUTs) in a direct product form, such as SU(5)⊗SU(3)F, SO(10)⊗SU(3)F or E(6)⊗SU(3)F, and also as a subgroup of the extended (family unified) SU(8) or E(8) GUTs; (v) It has a straightforward extension to the supersymmetric Standard Model and GUTs. With these natural criteria accepted, other family symmetry candidates are turned out to be at least partially discriminated.
Among the applications of the SU(3)F symmetry, the most interesting ones are the realistic description of the quark and lepton masses and mixings, neutrino masses and oscillations, rare processes etc. with a natural suppression of all dangerous flavor-changing transitions. The special sector of applications is related to a new type of topological defects - flavored cosmic strings and monopoles appearing during the spontaneous violation of the SU(3)F which may be considered as possible candidates for the cold dark matter in the Universe.
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