GUT theories from Calabi-Yau 4-folds with SO(10) Singularities

TL;DR

This work presents a global F-theory construction of an $SO(10)$ GUT on a Calabi–Yau 4-fold with a $D_5$ singularity, resolving the geometry through five blowups to obtain a smooth $ ilde{Y}_4$ and identifying the $oldsymbol{16}$ and $oldsymbol{10}$ matter curves as well as the Yukawa point at the $E_7$ enhancement. It develops both local and global $G$-fluxes, deriving quantization and orthogonality constraints, and demonstrates that, under parity conditions on the base data, the global flux matches the local expectations and yields the correct chiralities on matter curves (notably $oldsymbol{16}$) while highlighting the need for a factorised spectral cover to fix the $oldsymbol{10}$ chirality. The analysis reveals intricate features of the $D_5$ resolution, including an $E_7$-like enhancement with seven components rather than eight and a D7-enhancement that merges the two $oldsymbol{10}$ curves, providing insight into global vs local descriptions in $SO(10)$ F-theory GUTs. Overall, the paper bridges semi-local results with a fully global geometric and flux data framework, enabling controlled chiral spectrum engineering in this class of models.

Abstract

We consider an SO(10) GUT model from F-theory compactified on an elliptically fibered Calabi-Yau with a D5 singularity. To obtain the matter curves and the Yukawa couplings, we use a global description to resolve the singularity. We identify the vector and spinor matter representations and their Yukawa couplings and we explicitly build the G-fluxes in the global model and check the agreement with the semi-local results. As our bundle is of type SU(2k), some extra conditions need to be applied to match the fluxes.