Abstract
We present a detailed analysis of the eclectic flavor structure of the two-dimensional ℤ2 orbifold with its two unconstrained moduli T and U as well as SL(2, ℤ)T× SL(2, 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, mathcal{CP} and R-symmetries on the superpotential and Kähler potential of the theory.
Highlights
In this paper we extend our previous discussion [1] of the T2/Z2 orbifold
We present a detailed analysis of the eclectic flavor structure of the twodimensional Z2 orbifold with its two unconstrained moduli T and U as well as SL(2, Z)T × SL(2, Z)U modular symmetry
Once they are taken into account, we find an extension of the finite modular flavor symmetry in form of an R-symmetry, which implies further restrictions to the superpotential and Kähler potential of the theory
Summary
In this paper we extend our previous discussion [1] of the T2/Z2 orbifold. T2/Z2 is the only two-dimensional orbifold with two unconstrained moduli T , U that transform under SL(2, Z)T × SL(2, Z)U and under mirror symmetry, which interchanges T and U. We discuss the implications of these automorphy factors in the case of the T2/Z2 orbifold Once they are taken into account, we find an extension of the finite modular flavor symmetry in form of an R-symmetry, which implies further restrictions to the superpotential and Kähler potential of the theory. The additional R-symmetry is closely related to the modular symmetry and leads to further constraints on the allowed values of modular weights of matter fields We identify the additional R-symmetry and the extended eclectic flavor group This includes a discussion of the interplay of the modular weights with both, T ↔ U mirror symmetry and the R-symmetry. Technical details are relegated to several appendices that complete the general discussion of ref. [1]
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