Right-handed neutrinos and $U{\left(1\right)}_X$ symmetry-breaking

Abstract

The authors have proposed a global model for Heterotic $F$-theory duality with Wilson line symmetry-breaking and a $4+1$ split of the $F$-theory spectral divisor. Goals of this note are to treat the existence of right-handed neutrinos in our $F$-theory model, show that the ${\mathbb{Z}}_2$-action in our model breaks the $U{\left(1\right)}_X$-symmetry associated to the $4+1$ split to ${\mathbb{Z}}_2$-matter parity, and to identify Yukawa couplings for the MSSM matter fields.

15 pages