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

TL;DR

This work provides a systematic route to lift perturbative IIB O7/O3 models with permutation involutions to compact F-theory fourfolds by orbifolding CY3 bases to obtain CY4 bases, and validates the global construction through exact D3-tadpole matching. It then develops an intuitive, stack-by-stack method to engineer SU(5) enhancements in Weierstrass models, via Sen’s limit and a composition rule for D7-brane stacks, enabling explicit global realizations of GUT-like configurations. The results include a concrete SU(5) example on a permutation-involuted $Q^{(dP_7)^2}$ with detailed gauge-branch structure, and a two-stack generalization that avoids excessive brane counting while maintaining correct singularity types. Together, these methods bridge local F-theory intuition and global CY4 geometry, offering a blueprint for global perturbative lifts and phenomenologically relevant GUT models, with implications for fluxes and moduli stabilization in future work.

Abstract

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 smooth 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.