Grand Unification with Three Generations in Free Fermionic String Models

TL;DR

This paper explores constructing three-generation grand unified string models using free fermionic methods, successfully finding models with SU(5) but not with SO(10).

Contribution

It demonstrates the feasibility of creating three-generation models with SU(5) GUT groups in free fermionic string constructions.

Findings

Found three-generation models with SU(5) GUT group.

Did not find three-generation models with SO(10) GUT group.

Models with G×G structure enable necessary Higgs representations.

Abstract

We examine the problem of constructing three generation free fermionic string models with grand unified gauge groups. We attempt the construction of $G\times G$ models, where $G$ is a grand unified group realized at level 1. This structure allows those Higgs representations to appear which are necessary to break the symmetry down to the standard model gauge group. For $G=SO(10)$, we find only models with an even number of generations. However, for $G=SU(5)$ we find a number of 3 generation models.