Hypercharge Flux in IIB and F-theory: Anomalies and Gauge Coupling Unification

TL;DR

This work addresses how hypercharge flux can break GUT groups in Type IIB and F-theory without inducing a Stückelberg mass for $U(1)_Y$, while simultaneously managing anomalies and gauge coupling unification. By analyzing global Type IIB setups, the authors show that hypercharge flux can nontrivially restrict to orientifold-odd matter curves, with Green-Schwarz cancellation involving geometrically massive U(1)s, enabling realizations of a global ${U(1)}_{PQ}$-like symmetry alongside doublet-triplet splitting and no exotics. They further demonstrate that tree-level gauge coupling splitting can be reduced by a twisting of the flux and that, when the flux restricts to matter curves, the splitting becomes moduli-dependent and tied to moduli stabilisation in the F-theory uplift. The results imply relaxed anomaly constraints for F-theory GUTs with massive U(1)s and offer concrete IIB model examples that inform global F-theory constructions, potentially improving prospects for realistic unification and low-energy spectra.

Abstract

We analyse hypercharge flux GUT breaking in F-theory/Type IIB GUT models with regards to its implications for anomaly cancellation and gauge coupling unification. To this aim we exploit the Type IIB limit and consider 7-brane configurations that for the first time are guaranteed to exhibit net hypercharge flux restriction to matter curves. We show that local F-theory models with anomalies of type U(1)_Y-U(1)^2 in the massless spectrum can be consistent only if such additional U(1)s are globally geometrically massive (in the sense that they arise from non-Kahler deformations of the Calabi-Yau four-fold). Further, in such cases of geometrically massive U(1)s hypercharge flux can induce new anomalies of type U(1)_Y^2-U(1) in the massless spectrum, violating constraints in local models forbidding such anomalies. In particular this implies that it is possible to construct models exhibiting a U(1)_{PQ} global symmetry which have hypercharge flux doublet-triplet splitting and no further exotics. We also show that the known hypercharge flux induced splitting of the gauge couplings in IIB models at tree-level can be reduced by a factor of 5 by employing a more F-theoretic twisting of U(1) flux by hypercharge flux bringing it to well within MSSM 2-loop results. In the case of net restriction of hypercharge flux to matter curves this tree-level splitting becomes more involved, is tied to the vacuum expectation values of certain closed-string fields, and therefore gauge coupling unification becomes tied to the question of moduli stabilisation.