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

Understand

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'.