Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs

TL;DR

This paper investigates the constraints on embedding local F-theory GUT models into compactifications, constructing explicit three-generation models, and analyzing the role of spectral covers and fluxes in achieving realistic phenomenology.

Contribution

It provides a detailed analysis of spectral cover constraints in F-theory GUTs and introduces the necessity of incomplete GUT multiplets for consistent gauge coupling unification.

Findings

Spectral cover constraints conflict with certain neutrino scenarios unless additional fields are introduced.

Additional incomplete GUT multiplets are required below the GUT scale for gauge coupling unification.

Hypercharge flux effects can be canceled by these additional fields, maintaining unification.

Abstract

We analyze constraints for embedding local SU(5) F-theory GUTs into consistent compactifications and construct explicit three-generation models based on the geometry of arXiv:0904.3932. The key tool for studying constraints in this problem when there is an underlying E_8 structure is the spectral cover, which encodes all of the symmetries that fix the allowed couplings in the superpotential, as well as the consistent, supersymmetric G-fluxes. Imposing phenomenological requirements such as the existence of three generations, top and bottom Yukawa couplings, good flavor structure and absence of exotics and of a tree-level mu-term, we derive stringent constraints on the allowed spectral covers. The resulting spectral covers are in conflict with the neutrino scenarios that have been studied in local F-theory models unless we allow for the possibility of additional charged fields, perhaps playing the role of gauge messengers, that do not comprise complete GUT multiplets. Quite remarkably, the existence of additional incomplete GUT multiplets below the GUT scale is necessary for consistency with gauge coupling "unification", as their effect on weak scale couplings can precisely cancel that of the internal hypercharge flux, which distorts the gauge couplings already at M_GUT.