Yukawa hierarchies at the point of $E_8$ in F-theory

TL;DR

This paper investigates how different T-brane configurations in F-theory models with $E_8$ symmetry breaking to SU(5) influence Yukawa coupling hierarchies, identifying configurations that can produce realistic fermion mass patterns.

Contribution

It demonstrates that the hierarchy of fermion masses depends on the specific T-brane configuration, and identifies conditions under which realistic fermion masses can be achieved in F-theory GUTs.

Findings

Different T-brane configurations yield distinct Yukawa hierarchies.

Only some configurations can fit observed fermion masses with reasonable parameters.

Realistic charged fermion masses are achievable in a specific $E_8$ model.

Abstract

We analyse the structure of Yukawa couplings in local SU(5) F-theory models with $E_8$ enhancement. In this setting the $E_8$ symmetry is broken down to SU(5) by a 7-brane configuration described by T-branes, all the Yukawa couplings are generated in the vicinity of a point and only one family of quarks and leptons is massive at tree-level. The other two families obtain their masses when non-perturbative effects are taken into account, being hierarchically lighter than the third family. However, and contrary to previous results, we find that this hierarchy of fermion masses is not always appropriate to reproduce measured data. We find instead that different T-brane configurations breaking $E_8$ to SU(5) give rise to distinct hierarchical patterns for the holomorphic Yukawa couplings. Only some of these patterns allow to fit the observed fermion masses with reasonable local model parameter values, adding further constraints to the construction of F-theory GUTs. We consider an $E_8$ model where such appropriate hierarchy is realised and compute its physical Yukawas, showing that realistic charged fermions masses can indeed be obtained in this case.