Completing the eclectic flavor scheme of the ${\mathbb{Z}}_2$ orbifold

Abstract

We present a detailed analysis of the eclectic flavor structure of the two-dimensional ${\mathbb{Z}}_2$ orbifold with its two unconstrained moduli $T$ and $U$ as well as $\mathrm{SL}(2,\mathbb{Z}{)}_T\times \mathrm{SL}(2,\mathbb{Z}{)}_U$ modular symmetry. This provides a thorough understanding of mirror symmetry as well as the $R$-symmetries that appear as a consequence of the automorphy factors of modular transformations. It leads to a complete picture of local flavor unification in the $(T,U)$ modulus landscape. In view of applications towards the flavor structure of particle physics models, we are led to top-down constructions with high predictive power. The first reason is the very limited availability of flavor representations of twisted matter fields as well as their (fixed) modular weights. This is followed by severe restrictions from traditional and (finite) modular flavor symmetries, mirror symmetry, CP and $R$-symmetries on the superpotential and Kaehler potential of the theory.

arXiv comment46 pages, 3 figures 5 tables

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• Quasi-Eclectic Modular Flavor Symmetries
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Orbifolds from $\mathrm{Sp}(4,\mathbb{Z})$ and their modular symmetries
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