Family symmetries in F-theory GUTs

TL;DR

The paper investigates how local F-theory GUTs with explicit family symmetries can reproduce the observed fermion mass hierarchies and mixing patterns. It presents two concrete realizations: a flipped SU(5) model with U(1) chi and SU(4) perp monodromy giving a U(1) perp^2 family symmetry, and an SU(5) model with SU(5) × SU(5) perp and U(1) perp^3 symmetry combined with an R-parity from Calabi–Yau flux. In both, a leading-order rank-one Yukawa structure is achieved, with light generations arising from spontaneous breaking via a small set of familon vevs, and neutrino masses generated through see-saw with bi-large mixing. The work also addresses proton decay suppression, the μ-term, and FCNC constraints within the geometric monodromy framework. Overall, it demonstrates how flavor hierarchies can emerge in local F-theory GUTs without heavy reliance on flux corrections, using controlled monodromies and family symmetries to realize phenomenologically viable textures.

Abstract

We discuss F-theory SU(5) GUTs in which some or all of the quark and lepton families are assigned to different curves and family symmetry enforces a leading order rank one structure of the Yukawa matrices. We consider two possibilities for the suppression of baryon and lepton number violation. The first is based on Flipped SU(5) with gauge group SU(5)\times U(1)_χ\times SU(4)_{\perp} in which U(1)_χ plays the role of a generalised matter parity. We present an example which, after imposing a Z_2 monodromy, has a U(1)_{\perp}^2 family symmetry. Even in the absence of flux, spontaneous breaking of the family symmetry leads to viable quark, charged lepton and neutrino masses and mixing. The second possibility has an R-parity associated with the symmetry of the underlying compactification manifold and the flux. We construct an example of a model with viable masses and mixing angles based on the gauge group SU(5)\times SU(5)_{\perp} with a U(1)_{\perp}^3 family symmetry after imposing a Z_2 monodromy.