New F-theory lifts II: permutation orientifolds and enhanced singularities

In this paper, a procedure is developed to construct compact F-theory fourfolds corresponding to perturbative IIB O7/O3 models on CICY threefolds with permutation involutions. The method is explained in generality, and then applied to specific examples where the involution permutes two Del Pezzo surfaces. The fourfold construction is successfully tested by comparing the D3 charges predicted by F-theory and IIB string theory. The constructed fourfolds are then taken to the locus in moduli space where they have enhanced SU(5) singularities. A general, intuitive method is developed for engineering the desired singularities in Weierstrass models for complicated D7-brane setups.