MSSM from F-theory SU(5) with Klein Monodromy

We revisit a class of $SU(5)$ SUSY GUT models which arise in the context of the spectral cover with Klein Group monodromy $V_4=Z_2\times Z_2$. We show that $Z_2$ matter parities can be realised via new geometric symmetries respected by the spectral cover. We discuss a particular example of this kind, where the low energy effective theory below the GUT scale is just the MSSM with no exotics and standard matter parity, extended by the seesaw mechanism with two right-handed neutrinos.