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We study discrete flavor symmetries of the models based on a ten-dimensionalsupersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. Weassume non-vanishing non-factorizable fluxes as well as the orbifoldprojections. These setups allow model-building with more various flavorstructures. Indeed, we show that there exist various classes of non-Abeliandiscrete flavor symmetries. In particular, we find that $S_3$ flavor symmetriescan be realized in the framework of the magnetized 10D SYM theory for the firsttime.

Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions