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 have turned out to be at least partially discriminated.[clarification needed]
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[clarification needed] flavor-changing transitions. The special sector of applications is related to a newly described 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.
- Khlopov, Maxim Yu (1999). Cosmoparticle Physics. Singapore: World Scientific. p. 577. ISBN 9810231881.
- King, S.F.; Ross, G.G. (November 2001). "Fermion masses and mixing angles from SU(3) family symmetry". Physics Letters B. 520 (3–4): 243–253. arXiv:hep-ph/0108112. Bibcode:2001PhLB..520..243K. doi:10.1016/S0370-2693(01)01139-X. S2CID 6510221.
- Appelquist, Thomas; Bai, Yang; Piai, Maurizio (15 August 2005). "Breaking discrete symmetries in broken gauge theories". Physical Review D. 72 (3): 036005. arXiv:hep-ph/0506137. Bibcode:2005PhRvD..72c6005A. doi:10.1103/PhysRevD.72.036005. S2CID 119330778.
- Chkareuli, J. L. (1 December 1980). "Quark-lepton families: from SU(5) to SU(8) symmetry" (PDF). Soviet Journal of Experimental and Theoretical Physics Letters. 32 (11): 671–674. Bibcode:1980JETPL..32..671C. ISSN 0021-3640. DESY-L-TRANS-253.
- Wilczek, Frank (1983). "Thoughts on family symmetries preprint NSF-ITP-83-08". AIP Conference Proceedings. 96: 313. Bibcode:1983AIPC...96..313W. doi:10.1063/1.33949.
- Z.G. Berezhiani; J.L. Chkareuli (1983). "Quark-Lepton Families in a Model with SU(5)⊗SU(3) Symmetry". Sov. J. Nucl. Phys. 37 (4): 618.
- Berezhiani, Z.G. (September 1983). "The weak mixing angles in gauge models with horizontal symmetry — A new approach to quark and lepton masses". Physics Letters B. 129 (1–2): 99–102. Bibcode:1983PhLB..129...99B. doi:10.1016/0370-2693(83)90737-2.
- P. Ramond (1998). "The Family Group in Grand Unified Theories". arXiv:hep-ph/9809459. Bibcode:1998hep.ph....9459R. Cite journal requires
- Chkareuli, J.L.; Froggatt, C.D.; Nielsen, H.B. (April 2002). "Minimal mixing of quarks and leptons in the SU(3) theory of flavour". Nuclear Physics B. 626 (1–2): 307–343. arXiv:hep-ph/0109156. Bibcode:2002NuPhB.626..307C. CiteSeerX 10.1.1.346.7711. doi:10.1016/S0550-3213(02)00032-9. S2CID 9421103.
- Spergel, David; Pen, Ue-Li (20 December 1997). "Cosmology in a String-Dominated Universe". The Astrophysical Journal. 491 (2): L67–L71. arXiv:astro-ph/9611198. Bibcode:1997ApJ...491L..67S. doi:10.1086/311074. S2CID 388418.