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Compact F-theory GUTs with U(1)_PQ

Joseph Marsano, Natalia Saulina, Sakura Schafer-Nameki

TL;DR

This work builds semi-local and global F-theory constructions of SU(5) GUTs that incorporate a U(1)_{PQ} symmetry to suppress dimension-four proton decay and address the μ-term problem. The authors show that PQ symmetry inevitably introduces non-GUT exotics when SU(5) is broken by hypercharge flux, but argue these exotics can simultaneously resolve gauge-unification tensions (F-unification) and serve as potential gauge-mediation messengers. A detailed 3+2 spectral-cover framework is developed to realize three generations with a minimal set of exotics, including flux choices that satisfy D3-tadpole constraints without anti-D3-branes in several cases. The paper also analyzes singlet fields and their zero-mode counting, linking semi-local expectations to global geometry, and discusses how singlets could play roles as right-handed neutrinos or as mediators in SUSY breaking. Overall, the work demonstrates a constrained, globally consistent path to PQ-protected F-theory GUTs with rich phenomenology and testable implications for unification and SUSY breaking mediation.

Abstract

We construct semi-local and global realizations of SU(5) GUTs in F-theory that utilize a U(1)_PQ symmetry to protect against dimension four proton decay. Symmetries of this type, which assign charges to H_u and H_d that forbid a tree level μterm, play an important role in scenarios for neutrino physics and gauge mediation that have been proposed in local F-theory model building. As demonstrated in arXiv:0906.4672, the presence of such a symmetry implies the existence of non-GUT exotics in the spectrum, when hypercharge flux is used to break the GUT group and to give rise to doublet-triplet splitting. These exotics are of precisely the right type to solve the unification problem in such F-theory models and might also comprise a non-standard messenger sector for gauge mediation. We present a detailed description of models with U(1)_PQ in the semi-local regime, which does not depend on details of any specific Calabi-Yau four-fold, and then specialize to the geometry of arXiv:0904.3932 to construct three-generation examples with the minimal allowed number of non-GUT exotics. Among these, we find a handful of models in which the D3-tadpole constraint can be satisfied without requiring the introduction of anti-D3-branes. Finally, because SU(5) singlets that carry U(1)_PQ charge may serve as candidate right-handed neutrinos or can be used to lift the exotics, we study their origin in compact models and motivate a conjecture for how to count their zero modes in a semi-local setting.

Compact F-theory GUTs with U(1)_PQ

TL;DR

This work builds semi-local and global F-theory constructions of SU(5) GUTs that incorporate a U(1)_{PQ} symmetry to suppress dimension-four proton decay and address the μ-term problem. The authors show that PQ symmetry inevitably introduces non-GUT exotics when SU(5) is broken by hypercharge flux, but argue these exotics can simultaneously resolve gauge-unification tensions (F-unification) and serve as potential gauge-mediation messengers. A detailed 3+2 spectral-cover framework is developed to realize three generations with a minimal set of exotics, including flux choices that satisfy D3-tadpole constraints without anti-D3-branes in several cases. The paper also analyzes singlet fields and their zero-mode counting, linking semi-local expectations to global geometry, and discusses how singlets could play roles as right-handed neutrinos or as mediators in SUSY breaking. Overall, the work demonstrates a constrained, globally consistent path to PQ-protected F-theory GUTs with rich phenomenology and testable implications for unification and SUSY breaking mediation.

Abstract

We construct semi-local and global realizations of SU(5) GUTs in F-theory that utilize a U(1)_PQ symmetry to protect against dimension four proton decay. Symmetries of this type, which assign charges to H_u and H_d that forbid a tree level μterm, play an important role in scenarios for neutrino physics and gauge mediation that have been proposed in local F-theory model building. As demonstrated in arXiv:0906.4672, the presence of such a symmetry implies the existence of non-GUT exotics in the spectrum, when hypercharge flux is used to break the GUT group and to give rise to doublet-triplet splitting. These exotics are of precisely the right type to solve the unification problem in such F-theory models and might also comprise a non-standard messenger sector for gauge mediation. We present a detailed description of models with U(1)_PQ in the semi-local regime, which does not depend on details of any specific Calabi-Yau four-fold, and then specialize to the geometry of arXiv:0904.3932 to construct three-generation examples with the minimal allowed number of non-GUT exotics. Among these, we find a handful of models in which the D3-tadpole constraint can be satisfied without requiring the introduction of anti-D3-branes. Finally, because SU(5) singlets that carry U(1)_PQ charge may serve as candidate right-handed neutrinos or can be used to lift the exotics, we study their origin in compact models and motivate a conjecture for how to count their zero modes in a semi-local setting.

Paper Structure

This paper contains 51 sections, 236 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Symmetries and Proton Decay Operators
  3. Models with $PQ$ Symmetries
  4. Lifting the Exotics
  5. Importance of Global Models
  6. Summary and Outline
  7. Semi-local Model
  8. Definitions and General Properties
  9. Constraints from Phenomenology and F-unification
  10. Semi-local and Global Models with $U(1)_{PQ}$
  11. ${\bf 3 +2}$ factored spectral cover
  12. Monodromies and $U(1)_{PQ}$
  13. Neutrino Physics
  14. Matter curves and Yukawas in $S_{\rm GUT}$
  15. Matter Curves in the Spectral Cover
  16. ...and 36 more sections

Figures (3)

  • Figure 1: Affine $E_8$ Dynkin diagram
  • Figure 2: Five-sheeted spectral cover labeled by $\lambda_i$. Generically these sheets will be connected by branch-cuts, leading to a factorization of the spectral cover into the connected pieces. The right hand picture shows a $3+2$ factored spectral cover over $S_{\rm GUT}$.
  • Figure :