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

TL;DR

This paper investigates hypercharge flux effects in F-theory and Type IIB GUT models, focusing on anomaly cancellation and gauge coupling unification, revealing new constraints and potential for realistic model building.

Contribution

It demonstrates that hypercharge flux can induce anomalies and affect gauge coupling unification, with implications for global U(1) symmetries and model consistency.

Findings

Hypercharge flux can cause new anomalies in massless spectra.

Geometrically massive U(1)s are necessary for anomaly cancellation.

Gauge coupling splitting can be reduced by F-theoretic flux twisting.

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.