Froggatt-Nielsen meets Mordell-Weil: A Phenomenological Survey of Global F-theory GUTs with U(1)s

TL;DR

This work evaluates global F-theory GUTs with abelian U(1) symmetries by leveraging a modern classification of U(1) charges arising from smooth rational sections (the Mordell–Weil group). Imposing an exotic-free MSSM spectrum, hypercharge-flux anomaly cancellation, proton-decay suppression, and a Froggatt–Nielsen mechanism to generate full Yukawa textures, the authors identify a very small set of viable charge assignments, matter localizations, and geometric realizations. Notably, models with two U(1)s admit realistic quark and lepton textures (including CKM/PMNS structures) while single-U(1) scenarios are highly constrained or flavor-poor; two explicit FN-type classes (Haba/BaEnGo) emerge as phenomenologically viable, with detailed flavor, neutrino, and proton-decay analyses. The paper also outlines concrete geometric realizations for these viable charge patterns, linking them to specific elliptic-fibration fibers and non-canonical Tate structures, and provides a roadmap for constructing globally consistent FC-theory vacua with suitable GUT-breaking fluxes and U(1) charges.

Abstract

In F-theory, U(1) gauge symmetries are encoded in rational sections, which generate the Mordell-Weil group of the elliptic fibration of the compactification space. Recently the possible U(1) charges for global SU(5) F-theory GUTs with smooth rational sections were classified arXiv:1504.05593 [hep-th]. In this paper we utilize this classification to probe global F-theory models for their phenomenological viability. After imposing an exotic-free MSSM spectrum, anomaly cancellation (related to hypercharge flux GUT breaking in the presence of U(1) gauge symmetries), absence of dimension four and five proton decay operators and other R-parity violating couplings, and the presence of at least the third generation top Yukawa coupling, we generate the remaining quark and lepton Yukawa textures by a Froggatt-Nielsen mechanism. In this process we require that the dangerous couplings are forbidden at leading order, and when re-generated by singlet vevs, lie within the experimental bounds. We scan over all possible configurations, and show that only a small class of U(1) charge assignments and matter distributions satisfy all the requirements. The solutions give rise to the exact MSSM spectrum with realistic quark and lepton Yukawa textures, which are consistent with the CKM and PMNS mixing matrices. We also discuss the geometric realization of these models, and provide pointers to the class of elliptic fibrations with good phenomenological properties.

Figures (4)

• Figure 1: Process giving rise to dimension five proton decay parameterized by $\delta^1_{11aI}$.
• Figure 2: The configurations of fibers for an $SU(5)$ model with one $U(1)$ symmetry. The $I_5$ fiber, realized by the five black lines (corresponding to $\mathbb{P}^1$s in the fiber) gives rise to the $SU(5)$ gauge bosons, and the sections, shown as colored dots corresponding to the zero-section (blue) and the additional section (yellow), give rise to the additional abelian gauge factor.
• Figure 3: The configurations of fibers for an $SU(5)$ model with two $U(1)$ symmetries. The $I_5$ fiber, realized by the five black lines (corresponding to $\mathbb{P}^1$s in the fiber) gives rise to the $SU(5)$ gauge bosons, and the sections, shown as colored dots corresponding to the zero-section (blue) and the two additional sections (red, yellow), give rise to the additional abelian gauge factors.
• Figure 4: Fibers for the F-theoretic FN-model (Haba2) of table \ref{['tab:E8']}. The codimension one type $I_5^{(02|1)}$ is as in figure \ref{['fig:I5twoSec']} (up to permutation of the two extra sections), with the zero-section shown in blue. The nomenclature is as in Lawrie:2015hia: The codimension two fibers realizing the ${\bf \bar{5}}$ matter ($I_6$) as well as ${\bf 10}$ matter ($I_1^*$ fibers) are shown together with their charges. The coloring correspond to the wrapping of the fibers, and the labels along the wrapped components correspond to the degrees of the normal bundle, which in turn determine the charges. For the ${\bf \bar{5}}$ matter, the blue and yellow sections have to have the same configurations, as the charge is zero. These are shown in terms of green coloring. The blue/yellow colored representation graphs (box graphs) indicate the phases of the respective resolution type, see Hayashi:2014kca.