Landscaping with fluxes and the E8 Yukawa Point in F-theory

TL;DR

This work develops a rigorous, geometry-driven program to fix integral period bases for Calabi–Yau fourfolds relevant to F-theory, using Griffiths–Frobenius structure and homological mirror symmetry, and cross-checks via Gamma-class corrections and hemisphere localization. By classifying toric elliptic CY4s and employing sub-monodromy concepts, the authors show flux-induced stabilization of complex structure moduli at orbifold/gauge-enhancement loci, and demonstrate how SU(5) GUT models with an E8 Yukawa point can be embedded in global compactifications with explicit, calculable Yukawa and matter-curves data. They provide two detailed SU(5) examples, resolve high-codimension singularities, and analyze how nontrivial U(1) factors arise from extra sections, all within a framework that links heterotic duals, stable degeneration, and spectral-cover data. The results offer a concrete, modular toolkit for constructing phenomenologically relevant F-theory vacua with controlled moduli, gauge structure, and Yukawa couplings, grounded in exact period computations and automorphic structure. Overall, the paper advances the program of landscape landscaping by fluxes, delivering new computational control over moduli stabilization, gauge symmetry enhancements, and the precise organization of fourfold topological data through integral monodromy bases and HMS insights.

Abstract

Integrality in the Hodge theory of Calabi-Yau fourfolds is essential to find the vacuum structure and the anomaly cancellation mechanism of four dimensional F-theory compactifications. We use the Griffiths-Frobenius geometry and homological mirror symmetry to fix the integral monodromy basis in the primitive horizontal subspace of Calabi-Yau fourfolds. The Gamma class and supersymmetric localization calculations in the 2d gauged linear sigma model on the hemisphere are used to check and extend this method. The result allows us to study the superpotential and the Weil-Petersson metric and an associated tt* structure over the full complex moduli space of compact fourfolds for the first time. We show that integral fluxes can drive the theory to N=1 supersymmetric vacua at orbifold points and argue that fluxes can be chosen that fix the complex moduli of F-theory compactifications at gauge enhancements including such with U(1) factors. Given the mechanism it is natural to start with the most generic complex structure families of elliptic Calabi-Yau 4-fold fibrations over a given base. We classify these families in toric ambient spaces and among them the ones with heterotic duals. The method also applies to the creating of matter and Yukawa structures in F-theory. We construct two SU(5) models in F-theory with a Yukawa point that have a point on the base with an $E_8$-type singularity on the fiber and explore their embeddings in the global models. The explicit resolution of the singularity introduce a higher dimensional fiber and leads to novel features.

Figures (5)

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• Figure 3: Curves on the $q_0=0$ locus.
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