Hierarchies from D-brane instantons in globally defined Calabi-Yau Orientifolds

TL;DR

The paper tackles the challenge of generating stringy hierarchical couplings in globally consistent Type I vacua by employing $E1$-instantons on a Calabi-Yau threefold with magnetized D9-branes. By engineering the instanton zero-mode structure on rigid curves and ensuring tadpole cancellation and D-flatness, the authors build explicit global $SU(5)$-like models that realize both intermediate-scale Majorana masses for right-handed neutrinos and Polonyi-type SUSY breaking terms, with quantitative scales tied to the instanton volumes and gauge couplings. They demonstrate Majorana masses around $10^{10}$ GeV for a string scale $M_s \sim 10^{18}$ GeV and a GUT coupling $\alpha_{GUT}\sim 0.04$, and a Polonyi term suppressed by $e^{-S_{E1}} \sim 2.8\times 10^{-11}$ producing $F_\Phi \sim 10^{-11} M_s^2$, illustrating how non-perturbative string effects can generate phenomenologically relevant hierarchies. The work provides a concrete framework for embedding instanton-induced couplings in globally consistent vacua and suggests pathways to extend to other Yukawa couplings and $ $-term generation, with implications for moduli stabilization and SUSY-breaking mediation.

Abstract

We construct the first globally consistent semi-realistic Type I string vacua on an elliptically fibered manifold where the zero modes of the Euclidean D1-instanton sector allow for the generation of non-perturbative Majorana masses of an intermediate scale. In another class of global models, a D1-brane instanton can generate a Polonyi-type superpotential breaking supersymmetry at an exponentially suppressed scale.