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

TL;DR

This paper develops a comprehensive method using advanced geometric and physical tools to analyze fluxes, moduli stabilization, and Yukawa points in F-theory compactifications, enabling new insights into vacuum structure and gauge enhancements.

Contribution

It introduces a novel approach combining Griffiths-Frobenius geometry, mirror symmetry, and supersymmetric localization to study integral fluxes and moduli stabilization in Calabi-Yau fourfolds, with applications to F-theory model building.

Findings

Classified elliptic Calabi-Yau 4-fold families in toric spaces.

Constructed F-theory models with E8 Yukawa points and SU(5) gauge symmetry.

Demonstrated fluxes can fix complex moduli at gauge enhancement points.

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.