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

TL;DR

This paper explores how various non-abelian discrete flavor symmetries can emerge from different 2D orbifold compactifications, expanding the known set of symmetries relevant for particle physics models.

Contribution

It generalizes previous work by analyzing all possible 2D orbifolds and identifying the resulting non-abelian discrete flavor symmetries.

Findings

Identifies D3, D4, D6 symmetries from orbifolds

Shows these symmetries can originate from 6D to 4D compactification

Expands the set of flavor symmetries used in model building

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.