Journal of High Energy Physics 2016.3 (2016): 126 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)We analyse the structure of Yukawa couplings in local SU(5) F-theory models with E7 enhancement. These models are the minimal setting in which the whole flavour structure for the MSSM charged fermions is encoded in a small region of the entire compactification space. In this setup the E7 symmetry is broken down to SU(5) by means of a 7-brane T-brane background, and further to the MSSM gauge group by means of a hypercharge flux that also implements doublet-triplet splitting. At tree-level only one family of quarks and charged leptons is massive, while the other two obtain hierarchically smaller masses when stringy non-perturbative effects are taken into account. We find that there is a unique E7 model with such hierarchical flavour structure. The relative simplicity of the model allows to perform the computation of Yukawa couplings for a region of its parameter space wider than previous attempts, obtaining realistic fermion masses and mixings for large parameter regions. Our results are also valid for local models with E8 enhancement, pointing towards a universal structure to describe realistic fermion masses within this frameworkThis work has been partially supported by the grant FPA2012-32828 from the MINECO, the REA grant agreement PCIG10-GA-2011-304023 from the People Programme of FP7 (Marie Curie Action), the ERC Advanced Grant SPLE under contract ERC-2012-ADG-20120216-320421 and the grant SEV-2012-0249 of the “Centro de Excelencia Severo Ochoa” Programme. F.C. is supported through a fellowship of the international programme “La Caixa-Severo Ochoa”. F.M. is supported by the Ram´on y Cajal programme through the grant RYC-2009-05096. G.Z. is supported through a grant from “Campus Excelencia Internacional UAM+CSIC”. F.M. would like to thank HKUST IAS, the CERN TH Division, the Aspen Center for Theoretical Physics (supported through the NSF grant PHY-1066293) and UW-Madison for hospitality and support during the completion of this wor
