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

TL;DR

This paper explores a global F-theory model incorporating right-handed neutrinos, symmetry-breaking mechanisms, and Yukawa couplings, contributing to the understanding of particle physics within string theory frameworks.

Contribution

It introduces a specific F-theory model with a $4+1$ spectral divisor split, demonstrating how $ ext{Z}_2$-actions break $U(1)_X$ symmetry and identifying relevant Yukawa couplings.

Findings

Existence of right-handed neutrinos in the model.

Breaking of $U(1)_X$ symmetry to matter parity via $ ext{Z}_2$-action.

Identification of Yukawa couplings for MSSM matter fields.

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.