Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs
Joseph Marsano, Natalia Saulina, Sakura Schafer-Nameki
TL;DR
The paper investigates the constraints on embedding local $SU(5)$ F-theory GUTs into consistent compactifications using spectral covers and $G$-flux, aiming to realize a three-generation MSSM-like model. It finds a highly constrained set of monodromy groups and fluxes that can satisfy key phenomenological requirements, and demonstrates a concrete 3-generation compact example that captures the MSSM superpotential and GUT breaking but lacks a bare $ ext{mu}$ term. The analysis reveals tension with neutrino physics under exact $U(1)_{B-L}$ and suggests that introducing incomplete GUT multiplets (messengers) below the GUT scale could both preserve unification and provide the necessary flexibility. This points to a viable path for constructing fully realistic models by relaxing certain exotics constraints and incorporating carefully chosen messenger sectors, with broader implications for gauge coupling unification in F-theory GUTs.
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.