F-theory Compactifications for Supersymmetric GUTs

TL;DR

This work addresses the challenge of embedding realistic $SU(5)$ GUTs within globally consistent F-theory compactifications. It constructs elliptically fibered Calabi-Yau four-folds with an almost Fano base $X_3$, implements GUT breaking through hypercharge flux on a del Pezzo GUT surface, and demonstrates the possibility of obtaining three chiral MSSM generations via globally defined $G$-flux. It also shows how geometric constraints can mimic flavor hierarchies observed in local F-theory models, offering a bridge between local model phenomenology and global compactifications. The results advance the prospects for realistic Yukawa textures and proton-decay considerations within fully consistent string constructions.

Abstract

We construct a family of elliptically fibered Calabi-Yau four-folds Y_4 for F-theory compactifications that realize SU(5) GUTs in the low-energy limit. The three-fold base X_3 of these fibrations is almost Fano and satisfies the topological criteria required to ensure that the U(1)_Y gauge boson remains massless, while allowing a decoupling of GUT and Planck scale physics. We study generic features of these models and the ability to engineer three chiral generations of MSSM matter. Finally, we demonstrate that it is relatively easy to implement the topological conditions required to reproduce certain successful features of local F-theory models, such as the emergence of flavor hierarchies.

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