Abstract
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-Kähler 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 $ \mathrm{U}(1)_Y^2-\mathrm{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.
Highlights
As doublet-triplet splitting [1, 2]
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
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
Summary
Since we are primarily motivated by F-theory constructions we begin by summarising some of the relevant results in this setting. While (1.8) is in principle compatible with a non-trivial hypercharge flux restriction to the curves, more work is required to determine if the this restriction is non-vanishing In particular in such a local framework a complete analysis of the consistent types of splittings cannot be provided. Returning to the general models with only local splitting, the fact that the hypercharge flux must have no net restriction to the pull backs of the [bi] implies certain constraints on its possible net restriction to the [ci] and to the matter curves These were studied in [19, 25,26,27] and in particular in [28] it was shown for a general class of models (and later proven for all models in [29]) that the following constraints hold on the restriction to the matter curves. It is more likely that a whole new mechanism of hypercharge restriction in F-theory is avaialble as the uplift of our IIB results
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