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

Understand

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.