Non-Abelian Discrete Flavor Symmetries from T^2/Z_N Orbifolds

Abstract

In [1] it was shown how the flavor symmetry A4 (or S4) can arise if the three fermion generations are taken to live on the fixed points of a specific 2-dimensional orbifold. The flavor symmetry is a remnant of the 6-dimensional Poincare symmetry, after it is broken down to the 4-dimensional Poincare symmetry through compactification via orbifolding. This raises the question if there are further non-abelian discrete symmetries that can arise in a similar setup. To this end, we generalize the discussion by considering all possible 2-dimensional orbifolds and the flavor symmetries that arise from them. The symmetries we obtain from these orbifolds are, in addition to S4 and A4, the groups D3, D4 and D6 \simeq D3 x Z2 which are all popular groups for flavored model building.

12 pages, 4 figures

References in corpus (27)

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Cited by in corpus (14)

• Modular $A_4$ Symmetry Models of Neutrinos and Charged Leptons
• Trimaximal TM${}_1$ mixing with two modular $S_4$ groups
• Twin Modular $S_4$ with $SU(5)$ GUT
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Non-Abelian Discrete Groups from the Breaking of Continuous Flavor Symmetries
• [Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
• Flavour and CP predictions from orbifold compactification
• Modular flavour symmetry and orbifolds
• Exceptional Unification of Families and Forces
• Broken Symmetry as a Stabilizing Remnant
• Scotogenic majorana neutrino masses in a predictive orbifold theory of flavour
• Completing the eclectic flavor scheme of the ${\mathbb{Z}}_2$ orbifold
• Scotogenic dark matter in an orbifold theory of flavor
• Flavon alignments from orbifolding: $SU(5)\times SU(3)$ model with ${\mathbb{T}}^6/\Delta (54)$