Hypercharge Flux, Exotics, and Anomaly Cancellation in F-theory GUTs

TL;DR

The paper shows that constraints on hypercharge flux in F-theory GUTs with U(1) symmetries originate from 4D anomaly cancellation. It derives a generalized set of Dudas-Palti relations, tying the distribution of hypercharge flux across matter curves to MSSM anomaly cancellation and ensuring a massless hypercharge gauge boson. The results imply that, in flavor constructions using hypercharge flux, any extra U(1) symmetry compatible with the setup must be $U(1)_\chi$, while attempting a $U(1)_{PQ}$ symmetry generally yields charged exotics unless specific flux distributions are chosen. Overall, the work unifies spectral-cover observations with a 4D anomaly-based origin and delineates strict constraints for viable phenomenology in F-theory GUTs.

Abstract

We sharpen constraints related to hypercharge flux in F-theory GUTs that possess U(1) symmetries and argue that they arise as a consequence of 4-dimensional anomaly cancellation. This gives a physical explanation for all restrictions that were observed in spectral cover models while demonstrating that the phenomenological implications for a well-motivated set of models are not tied to any particular formalism.