Orbifold Modular GUT of Flavour

We discuss an $SU(5)$ Grand Unified Theory (GUT) based on the 10d orbifold $(\mathbb{T}^2)^3/(\mathbb{Z}_4\times\mathbb{Z}_2)$ plus three modular $S_4$ groups with moduli at respective fixed points $i,i+2,\omega=e^{2i\pi/3}$. The resulting model has hierarchical quark and charged lepton mass matrices, arising from a double weighton mechanism, and reproduces the highly predictive Littlest Seesaw Mechanism in the neutrino sector. The down quark mass matrix has an upper triangular form, contributing to CKM mixing, while the charged lepton mass matrix has a lower triangular form with suppressed contributions to PMNS mixing. The orbifold yields successful $SU(5)$ breaking with doublet-triplet splitting of the Higgs multiplets.