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We discuss the Yukawa couplings in 6D gauge-Higgs unification models on$T^2/Z_N$ in the presence of magnetic fluxes. We provide general formulae forthem, and numerically evaluate their magnitude in a specific model on$T^2/Z_3$. Thanks to the nontrivial profiles of the zero-mode wave functions,the top quark Yukawa coupling can be reproduced without introducing a largerepresentation of the gauge group for matter fields. However, it is difficultto realize small Yukawa couplings only by the magnetic fluxes and theWilson-line phases because of the complicated structure of the mode functionson $T^2/Z_N$ ($N=3,4,6$).

Yukawa couplings in 6D gauge-Higgs unification on $T^2/Z_N$ with magnetic fluxes