Family symmetries in F-theory GUTs

TL;DR

This paper explores how family symmetries in F-theory GUTs can lead to realistic fermion masses and mixings, proposing models with different symmetry structures and mechanisms for suppressing baryon and lepton number violation.

Contribution

It introduces novel F-theory GUT models with specific family symmetry assignments and mechanisms for mass generation and violation suppression, expanding the landscape of viable theories.

Findings

Viable quark, charged lepton, and neutrino masses achieved

Models with U(1) family symmetries after monodromy imposed

Suppression of baryon and lepton number violation demonstrated

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)_\chi \times SU(4)_{\perp} in which U(1)_{\chi} 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.