We analyze local models at the point of $E_8$ in $F$-theory grand unified theories and identify exactly two models with potentially realistic properties concerning proton stability and a suitable pattern of quark and lepton masses. To this end, we identify a matter parity at the local point. A globally consistent ultraviolet completion turns out to be problematic for both models. It is impossible to embed the models in a semilocal scheme via the spectral cover approach. This seems to severely limit the predictive power of local model building and to indicate that the full string theory might give us valuable hints for particle physics model building.

• Received 21 January 2011

DOI:https://doi.org/10.1103/PhysRevD.83.086008