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

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