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

TL;DR

This paper derives formulas for Yukawa couplings in 6D gauge-Higgs unification models on orbifolds with magnetic fluxes, demonstrating the potential to reproduce the top quark Yukawa coupling without large representations, but highlighting challenges in achieving small Yukawa couplings.

Contribution

It provides general formulae for Yukawa couplings in 6D models with magnetic fluxes on $T^2/Z_N$ and evaluates their magnitude in a specific $T^2/Z_3$ model.

Findings

Top Yukawa coupling can be reproduced without large gauge representations.

Magnetic fluxes and Wilson-line phases alone struggle to produce small Yukawa couplings.

Mode function complexity on $T^2/Z_N$ affects Yukawa coupling realization.

Abstract

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 for them, 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 large representation of the gauge group for matter fields. However, it is difficult to realize small Yukawa couplings only by the magnetic fluxes and the Wilson-line phases because of the complicated structure of the mode functions on $T^2/Z_N$ ($N=3,4,6$).