GUTs and Exceptional Branes in F-theory - II: Experimental Predictions

TL;DR

The paper develops a bottom-up framework for realizing Grand Unified Theories in F-theory by wrapping seven-branes on del Pezzo surfaces and breaking the GUT group via internal U(1) hypercharge flux. It demonstrates how this flux naturally solves doublet-triplet splitting, distorts lighter-generation GUT mass relations through Aharonov-Bohm effects, and yields nearly exact global symmetries that suppress unwanted operators and μ terms. The authors show how hierarchical Yukawas, neutrino masses, and viable gauge-mediated SUSY breaking can emerge from wave-function localization and flux geometry, while avoiding exotics in MSSM spectra. They provide explicit SU(5) and flipped SU(5) constructions, discuss discrete Wilson lines, and examine non-decoupled cases with surfaces of general type. Overall, the work argues that F-theory GUTs on del Pezzo surfaces offer a predictive, energetically consistent path toward realistic supersymmetric unification with testable phenomenology.

Abstract

We consider realizations of GUT models in F-theory. Adopting a bottom up approach, the assumption that the dynamics of the GUT model can in principle decouple from Planck scale physics leads to a surprisingly predictive framework. An internal U(1) hypercharge flux Higgses the GUT group directly to the MSSM or to a flipped GUT model, a mechanism unavailable in heterotic models. This new ingredient automatically addresses a number of puzzles present in traditional GUT models. The internal U(1) hyperflux allows us to solve the doublet-triplet splitting problem, and explains the qualitative features of the distorted GUT mass relations for lighter generations due to the Aharanov-Bohm effect. These models typically come with nearly exact global symmetries which prevent bare mu terms and also forbid dangerous baryon number violating operators. Strong curvature around our brane leads to a repulsion mechanism for Landau wave functions for neutral fields. This leads to large hierarchies of the form exp(-c/B^(2*g)) where c and g are order one parameters and B ~ M_(GUT)/(M_(pl)*alpha_(GUT)). This effect can simultaneously generate a viably small mu term as well as an acceptable Dirac neutrino mass on the order of 0.5 * 10^(-2 +/- 0.5) eV. In another scenario, we find a modified seesaw mechanism which predicts that the light neutrinos have masses in the expected range while the Majorana mass term for the heavy neutrinos is ~ 3 * 10^(12 +/- 1.5) GeV. Communicating supersymmetry breaking to the MSSM can be elegantly realized through gauge mediation. In one scenario, the same repulsion mechanism also leads to messenger masses which are naturally much lighter than the GUT scale.

Figures (8)

• Figure 1: General overview of how GUT breaking constrains the type of GUT model.
• Figure 2: Depiction of F-theory compactified on a local model of a Calabi-Yau fourfold with non-compact base threefold $B_{3}$. The diagram shows the behavior of the geometry in the neighborhood of a compact Kähler surface $S$ on which the gauge degrees of freedom of the GUT model can localize in the cases where $B_{3}$ is given by a roughly tubular geometry, as in case a), as well as geometries where $B_{3}$ is more homogeneous, as in case b). In both cases, the directions orthogonal to $S$ in $B_{3}$ are large compared to $S$, but not warped. To regulate the geometry of the local model it is necessary to introduce a cutoff length scale which we denote by $R_{\bot}$. The intersection locus between the compact surface $S$ and a non-compact surface $S^{\prime}$ appears as a curve $\Sigma$ in $S$. When seven-branes wrap both surfaces, additional light states will localize on this matter curve.
• Figure 3: The bulk group on the Kähler surface $S$ corresponds to a singularity of type $G_{S}$. Over complex codimension one matter curves in $S$ which we denote by $\Sigma$, this singularity type can further enhance so that six-dimensional matter fields localize on these curves. Over complex codimension two points in $S$ the singularity type can enhance further. On the left of the figure we depict a triple intersection of matter curves in $S$. It is also possible for one of the matter curves to intersect $S$ at a point. Depending on the background gauge fluxes and local curvatures, wave functions localized on curves normal to the GUT brane are either exponentially suppressed or of order one near the point of contact with the GUT brane.
• Figure 4: Letting $[F_{S}]$ denote the two-cycle in $H_{2}(S,\mathbb{Z} )$ which is Poincaré dual to the background hypercharge flux $\left\langle F_{S}\right\rangle$, there is a natural distinction between the class of the Higgs curve $[\Sigma_{H}]$ and the class of the chiral matter curves $[\Sigma_{M}]$. Indeed, while the net flux on $\Sigma_{M}$ must vanish to preserve a full GUT multiplet, the gauge field configuration must restrict non-trivially on the Higgs curves in order to solve the doublet triplet splitting problem. When the net flux on the Higgs curve is not zero, this corresponds to the condition that $[\Sigma_{M}]$ and $\left[ F_{S}\right]$ are orthogonal while $[\Sigma_{H}]$ and $\left[ F_{S}\right]$ are not.
• Figure 5: Depiction of how the geometry of matter curves directly translates into amplitudes in the low energy theory. In case a), the Higgs up and down fields localize on the same matter curve. The resulting field theory diagram which generates the operator $QQQL$ is given by interpreting each matter curve as the leg of a Feynman diagram. In case b), the Higgs up and down fields localize on distinct matter curves. In this case, the Feynman diagram involving the exchange of massive Higgs triplets is unavailable.