Classification of SU(4) X SU(2) X U(1) Heterotic-String Models

TL;DR

This paper classifies heterotic-string models with a specific gauge symmetry breaking pattern and demonstrates that this class cannot produce viable three-generation models, extending previous classifications to a new subgroup.

Contribution

It extends the classification of free fermionic heterotic-string models to the SU(4)×SU(2)_L×U(1)_R subgroup and shows this class cannot yield three-generation models.

Findings

Classified models with SU(4)×SU(2)_L×U(1)_R symmetry

Proved this class cannot produce viable three-generation models

Extended previous classifications to new gauge symmetry breaking pattern

Abstract

The free fermionic construction of the heterotic string in four dimensions produced a large space of three generation models with the underlying $SO(10)$ embedding of the Standard Model states. The $SO(10)$ symmetry is broken to a subgroup directly at the string scale. Over the past few years free fermionic models with the Pati-Salam and flipped $SU(5)$ subgroups have been classified. In this paper we extend this classification program to models in which the $SO(10)$ symmetry is broken at the string level to the $SU(4)\times SU(2)_L\times U(1)_R$ (SU421) subgroup. The subspace of free fermionic models that we consider corresponds to symmetric ${\mathbb{Z}}_2 \times {\mathbb{Z}}_2$ orbifolds. We provide a general argument that shows that this class of SU421 free fermionic models cannot produce viable three generation models.