Non-Abelian Discrete Groups from the Breaking of Continuous Flavor Symmetries

Abstract

We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying continuous, possibly gauged, flavor symmetry SU(2) or SU(3) through spontaneous symmetry breaking. We consider all possible cases, where the continuous symmetry is broken by small representations. "Small" representations are these which couple at leading order to the Standard Model fermions transforming as two- or three-dimensional representations of the flavor group. We find that, given this limited representation content, the only non-abelian discrete group which can arise as a residual symmetry is the quaternion group D_2'.

15 pages

References in corpus (6)

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• (Non-)Abelian discrete anomalies
• Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups
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• Generation Symmetry and E_6 Unification
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Cited by in corpus (7)

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• Simultaneous Block Diagonalization of Matrices of Finite Order
• Nonzero ${\theta }_{13}$ in $SO(3)\to A_4$ lepton models
• Symmetries from outer automorphisms and unorthodox group extensions