Breaking GUT groups in F-theory
We consider the possibility of breaking the GUT group to the Standard Model gauge group in $F$-theory compactifications by turning on certain $U(1)$ fluxes. We show that the requirement of massless hypercharge is equivalent to a topological constraint on the UV completion of the local model. The possibility of this mechanism is intrinsic to $F$-theory. We address some of the phenomenological signatures of this scenario. We show that our models predict monopoles as in conventional GUT models. We discuss in detail the leading threshold corrections to the gauge kinetic terms and their effect on unification. They turn out to be related to Ray–Singer torsion. We also discuss the issue of proton decay in $F$-theory models and explain how to engineer models which satisfy current experimental bounds.