A note on hypercharge flux, anomalies, and U(1)s in F-theory GUTs

We study the consequences of cancellation of cubic Abelian anomalies in F-theory grand unified theory (GUT) models that use 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, unless the local U(1)s are globally geometrically massive, there are only two possible classes of models in F-theory GUTs, which have fields on matter curves in noncomplete GUT representations that are not vectorlike 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 realizing models from F-theory GUTs like the next to minimal supersymmetric Standard Model.