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This paper shows that, a quasi-localization of wavefunctions in toroidalcompactifications with magnetic fluxes can lead to a strong suppression forrelevant Yukawa couplings, and it is applicable to obtain tiny neutrino masses.Although it is known that magnetic fluxes lead to a Gaussian profile ofzero-modes on a torus and that can yield a suppressed coupling inhigher-dimensional supersymmetric Yang-Mills (SYM) theories, the largest(diagonal) entry of Yukawa matrices is always of $\mathcal O(1)$. In thispaper, we propose a way to induce an absolutely tiny global factor of Yukawamatrices. In two SYM theories defined in different dimensional spacetime, theirbifundamental representations must be localized as a point in some directions.Overlaps of such point-like localized wavefunctions and Gaussian zero-modesgive a global factor of Yukawa matrices, and it can be a strong suppressionfactor or a usual $\mathcal O(1)$ factor, corresponding to their distance. Ournumerical analysis shows that it is possible to obtain a suppression strongenough to realize the tiny neutrino masses without a hard fine-tuning.Furthermore, we propose a concrete model of the tiny neutrino Yukawa couplingsin a magnetized SYM system.

Quasi-localized wavefunctions on magnetized tori and tiny neutrino Yukawa couplings