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Global F-theory GUTs

Ralph Blumenhagen, Thomas W. Grimm, Benjamin Jurke, Timo Weigand

TL;DR

Global F-theory GUTs are developed on complete-intersection Calabi-Yau fourfolds with del Pezzo GUT branes, enabling a global realization of $SU(5)$ GUTs with realistic matter content. The authors implement a split $S[U(4) imes U(1)_X]$ spectral cover to generate chiral spectra and suppress dangerous dimension-4 proton decay operators, while breaking to the MSSM via hypercharge flux. They introduce a toric-based toolkit and derive a closed expression for the Euler characteristic $oxed{ ext{χ}(Y)}$ of singular CY fourfolds, facilitating global tadpole checks. An explicit three-generation global model is constructed on a del Pezzo transition of the Fano threefold ${oldsymbol{ extbf P}}^4[4]$, with a complete-intersection CY fourfold and resolved $SU(5)$ singularities, achieving the required Yukawa couplings. The work demonstrates the feasibility of full global F-theory GUT constructions and highlights both the potential phenomenological successes and the remaining challenges, such as Higgs-sector tuning and precise tadpole balancing.

Abstract

We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi-Yau fourfolds realized as complete intersections of two hypersurface constraints. The intersections of the GUT brane and the flavour branes as well as the gauge flux are described by the spectral cover construction. We consider a split S[U(4) x U(1)_X] spectral cover, which allows for the phenomenologically relevant Yukawa couplings and GUT breaking to the MSSM via hypercharge flux while preventing dimension-4 proton decay. General expressions for the massless spectrum, consistency conditions and a new method for the computation of curvature-induced tadpoles are presented. We also provide a geometric toolkit for further model searches in the framework of toric geometry. Finally, an explicit global model with three chiral generations and all required Yukawa couplings is defined on a Calabi-Yau fourfold which is fibered over the del Pezzo transition of the Fano threefold P^4[4].

Global F-theory GUTs

TL;DR

Global F-theory GUTs are developed on complete-intersection Calabi-Yau fourfolds with del Pezzo GUT branes, enabling a global realization of GUTs with realistic matter content. The authors implement a split spectral cover to generate chiral spectra and suppress dangerous dimension-4 proton decay operators, while breaking to the MSSM via hypercharge flux. They introduce a toric-based toolkit and derive a closed expression for the Euler characteristic of singular CY fourfolds, facilitating global tadpole checks. An explicit three-generation global model is constructed on a del Pezzo transition of the Fano threefold , with a complete-intersection CY fourfold and resolved singularities, achieving the required Yukawa couplings. The work demonstrates the feasibility of full global F-theory GUT constructions and highlights both the potential phenomenological successes and the remaining challenges, such as Higgs-sector tuning and precise tadpole balancing.

Abstract

We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi-Yau fourfolds realized as complete intersections of two hypersurface constraints. The intersections of the GUT brane and the flavour branes as well as the gauge flux are described by the spectral cover construction. We consider a split S[U(4) x U(1)_X] spectral cover, which allows for the phenomenologically relevant Yukawa couplings and GUT breaking to the MSSM via hypercharge flux while preventing dimension-4 proton decay. General expressions for the massless spectrum, consistency conditions and a new method for the computation of curvature-induced tadpoles are presented. We also provide a geometric toolkit for further model searches in the framework of toric geometry. Finally, an explicit global model with three chiral generations and all required Yukawa couplings is defined on a Calabi-Yau fourfold which is fibered over the del Pezzo transition of the Fano threefold P^4[4].

Paper Structure

This paper contains 23 sections, 156 equations, 8 tables.

Table of Contents

  1. Introduction
  2. Compact geometries for GUT model building
  3. Calabi-Yau fourfold bases and del Pezzo transitions
  4. Complete-intersecting Calabi-Yau fourfolds
  5. Geometric tadpoles
  6. F-theory compactifications with $SU(5)$ gauge symmetry
  7. $SU(5)$ GUT models
  8. Spectral cover construction
  9. Gauge flux in generic $SU(5)$ GUT models
  10. GUT breaking by hypercharge flux via $S[U(5)\times U(1)]$ bundles
  11. $S[U(4)\times U(1)_X]$ split spectral covers
  12. Split spectral covers
  13. Split spectral cover bundle
  14. GUT symmetry breaking and 3-brane tadpole
  15. Supersymmetry condition and stable extensions
  16. ...and 8 more sections