In the Z3 heterotic orbifold, the modular symmetry of the Kähler modulus is Gamma(3), and the discrete flavor symmetry Delta(27) arises from misaligned U(1) gauge symmetries that become massless at different critical points.
Eclectic Flavor Groups
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abstract
The simultaneous study of top-down and bottom-up approaches to modular flavor symmetry leads necessarily to the concept of eclectic flavor groups. These are nontrivial products of modular and traditional flavor symmetries that exhibit the phenomenon of local flavor enhancement in moduli space. We develop methods to determine the eclectic flavor groups that can be consistently associated with a given traditional flavor symmetry. Applying these methods to a large family of prominent traditional flavor symmetries, we try to identify potential candidates for realistic eclectic flavor groups and show that they are relatively rare. Model building with finite modular flavor symmetries thus appears to be much more restrictive than previously thought.
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Flavor Symmetries and Winding Modes
In the Z3 heterotic orbifold, the modular symmetry of the Kähler modulus is Gamma(3), and the discrete flavor symmetry Delta(27) arises from misaligned U(1) gauge symmetries that become massless at different critical points.