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

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.

arXiv commentPublication Version (Notes: 16 Pages & References added)

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• The 750 GeV diphoton LHC excess and Extra Z's in Heterotic-String Derived Models
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• Classification of Left-Right Symmetric Heterotic String Vacua
• String Phenomenology From a Worldsheet Perspective
• The Flipped SU(5) String Vacua Classification: A Variation Of The SO(10) Breaking Basis Vector
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