The eclectic flavor symmetry of the ℤ2 orbifold

A bstract Modular symmetries naturally combine with traditional flavor and $$ \mathcal{CP} CP , giving rise to the so-called eclectic symmetry. We apply this scheme two-dimensional ℤ 2 orbifold, which is equipped two modular SL(2 ℤ) T U associated moduli: Kähler modulus complex structure . The resulting finite group (( S 3 × ) ⋊ 4 including mirror symmetry (that exchanges a generalized -transformation. Together ( D 8 )/ℤ leads huge 4608 elements. At specific regions in moduli space we observe enhanced unified as many 1152 elements for tetrahedral shaped orbifold \left\langle T\right\rangle =\left\langle U\right\rangle =\exp \left(\frac{\pi \mathrm{i}}{3}\right) T = U exp π i 3 This rich implies interesting (modular) groups particle physics models derived form string theory.