A Note on Hypercharge Flux, Anomalies, and U(1)s in F-theory GUTs

TL;DR

This paper analyzes the cancellation of cubic Abelian anomalies in F-theory GUT models employing hypercharge flux in the presence of additional U(1) symmetries. By deriving anomaly constraints on hypercharge-flux-induced chirality on 5- and 10-curves, it shows that certain U(1) embedding patterns are incompatible with anomaly cancellation, and identifies two viable GUT-breaking splits, 3+2 and 2+2+1, that admit nonzero hypercharge flux consistent with the constraints. The results imply that the up-type Higgs cannot carry hypercharge flux nontrivially, forcing Higgs fields to be vector-like under all U(1)s and often requiring TeV-scale exotics to realize NMSSM-like models, with a preferred exotic content that preserves perturbative gauge coupling unification. The work highlights a strong link between local anomaly structure and global U(1) physics, motivating further study of global F-theory constructions to realize these constraints in consistent compactifications.

Abstract

We study the consequences of cancellation of cubic Abelian anomalies in F-theory GUT models that utilise hypercharge flux in the presence of additional U(1) symmetries. We show that a mixed anomaly between the hypercharge and two U(1) gauge fields is not automatically canceled in local models based on the spectral cover and therefore imposes additional constraints on local models in F-theory that have not been accounted for so far. The constraints imply that there are only two possible classes of models in F-theory GUTs which have fields on matter curves in non-complete GUT representations that are not vector-like under all U(1)s: the ones based on a 3+2 and 2+2+1 split. We comment on some phenomenological implications of these results for realising NMSSM-like models from F-theory GUTs.