Decoupling Gravity in F-Theory

TL;DR

The work investigates local F-theory SU(5) GUT models in which gravity decouples from the gauge sector, showing that such decoupling imposes stringent geometric and topological constraints on the base X and the Weierstrass data of the elliptic Calabi–Yau fourfold. By analyzing volumes via a Calabi–Yau kinematic limit and applying Grauert/Mori theory, the authors rule out Fano threefold bases as UV completions and derive a priori constraints on seven-brane tadpoles and matter curves, linking local Yukawa couplings to global topology. They reveal that decoupled local models inexorably lack adjoint Higgs fields and exhibit exotic Yukawa structures, with non-perturbative effects and hidden sectors likely essential for viable phenomenology. The results connect anomaly-cancellation-like constraints with detailed brane intersections, and highlight how decoupling limits shape the spectrum and couplings, offering guidance for constructing globally consistent local F-theory GUTs with realistic features. Overall, the paper shows that gravity-weak decoupling both restricts the local model-building space and enriches the required physics with nontrivial global geometric interplay.

Abstract

We study seven-brane SU(5) GUT models of string phenomenology which can be consistently analyzed in a purely local framework. The requirement that gravity can decouple constrains the form of four-dimensional physics as well as the geometry of spacetime. We rule out a large family of candidate UV completions of such models and derive a priori constraints on the local singularities of compact elliptic Calabi-Yau fourfolds. These constraints are strong enough to obstruct a wide class of brane constructions from UV completion in string theory. It is demonstrated that consistent local models always have exotic Yukawa coupling structures, and hidden sectors or interesting non-perturbative superpotentials which merit further investigation.

Figures (4)

• Figure 1: The internal geometry of F-theory brane models and their various string sectors.
• Figure 2: A non-rigid cycle $S$ whose collapse would lead to the collapse of the three-dimensional striated region.
• Figure 3: An attempt to create a Fano threefold with a $dP_{2}$ which admits a decoupling limit by blowing up $\mathbb{P}^{3}$ twice. The construction fails because $c_{1}(X)$ is not positive on the proper transform of the line $L$.
• Figure 4: An example of a ruled surface $S$ is a $\mathbb{P}^{1}$ fibration over a curve of genus two. A seven-brane gauge theory compactified on $S$ would have a pair of phenomenologically undesirable light adjoint scalars.