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

TL;DR

This paper investigates anomaly cancellation constraints in F-theory GUT models with hypercharge flux and additional U(1) symmetries, revealing new restrictions on model classes and implications for phenomenology.

Contribution

It identifies previously unaccounted constraints from mixed anomaly cancellation that limit the classes of viable F-theory GUT models with hypercharge flux and extra U(1)s.

Findings

Only two classes of models (3+2 and 2+2+1 splits) satisfy anomaly cancellation.

Mixed hypercharge-U(1)-U(1) anomalies impose new constraints on local F-theory models.

Implications for constructing NMSSM-like models from F-theory GUTs.

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.