Particle Physics Implications of F-theory

TL;DR

F-theory GUTs provide a geometric, strongly coupled framework to realize Grand Unification on local seven-brane configurations, connecting string-scale physics to low-energy phenomenology. The review surveys the building blocks—elliptic F-theory geometry, fluxes on seven-branes, and 4D effective theory—and analyzes GUT breaking, proton decay constraints, gauge coupling unification, SUSY breaking mechanisms, and flavor generation via seven-brane monodromy. It highlights minimal $E_8$ unification as a highly predictive approach with distinctive experimental signatures, including quasi-stable NLSP scenarios and specific neutrino and dark matter expectations. The work underscores the tight interplay between geometry and phenomenology in these models and points to future directions in constructing explicit global geometries and testing them at colliders and beyond.

Abstract

We review recent progress in realizing Grand Unified Theories (GUTs) in a strongly coupled formulation of type IIB string theory known as F-theory. Our main emphasis is on the expected low-energy phenomenology of a minimal class of F-theory GUTs. We introduce the primary ingredients in such constructions, and then present qualitative features of GUT models in this framework such as GUT breaking, doublet-triplet splitting, and proton decay. Next, we review proposals for realizing flavor hierarchies in the quark and lepton sectors. We discuss possible supersymmetry breaking scenarios, and their consequences for experiment, as well as geometrically minimal realizations of F-theory GUTs which incorporate most of these features.

Figures (3)

• Figure 1: Depiction of an $E_{6}$ singularity enhancement. The ellipsoidal shape denotes the internal directions of the seven-brane, with gauge group $SU(5)$. Along complex one dimensional curves, the singularity enhances to $SO(10)$ and $SU(6)$, where matter in the $10$ and $5$ of $SU(5)$ respectively localize. There is a further enhancement to $E_{6}$ at a point of the geometry, where the Yukawa interaction $5_{H}\times10_{M}\times10_{M}$ localizes.
• Figure 2: Plot of the sparticle mass spectrum (indicated by $\widetilde{}$'s) in an F-theory GUT with one vector-like pair of messengers in the $10 \oplus \overline{10}$ and $F_X / x = 5 \times 10^4$ GeV for minimal (left, red columns) and maximal (right, blue columns) PQ deformation. At $\Delta^{min}_{PQ} = 0$, a bino-like lightest neutralino $\widetilde{\chi}^{0}_1$ is the NLSP. For moderate values of $\Delta_{PQ} \sim 100$ GeV, the NLSP transitions to the lightest stau $\widetilde{\tau}_1$, which persists until a tachyon develops near $\Delta^{max}_{PQ} \sim 200$ GeV.
• Figure 3: Depiction of a minimal model with $E_{8}$ point unification. In the proposed model, all of the interaction terms descend from a single $E_{8}$ point of enhancement. Here, matter curves inside the seven-brane are depicted by straight lines and curves normal to the seven-brane are depicted by cigar-shaped tubes. In these minimal models, there is typically just enough room to accommodate the MSSM spectrum, and a minimal messenger sector ($Y$'s) in the $10\oplus\overline{10}$.