Fitting fermion masses and mixings in F-theory GUTs

Abstract

We analyse the structure of Yukawa couplings in local SU(5) F-theory models with $E_7$ 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 $E_7$ 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 $E_7$ 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 $E_8$ enhancement, pointing towards a universal structure to describe realistic fermion masses within this framework.

66 pages, 7 figures. v2, corrected typos

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• Compact T-branes
• $E_6$ Yukawa couplings in F-theory as D-brane instanton effects
• T-branes and Matrix Models
• MSSM from F-theory SU(5) with Klein Monodromy
• The two faces of T-branes
• R-Parity violation in F-Theory
• Yukawa Hierarchies in Global F-theory Models
• T-branes and defects
• Towards natural and realistic $E_7$ GUTs in F-theory