A Classification of 3-Family Grand Unification in String Theory I. The SO(10) and E_6 Models

TL;DR

This paper classifies 3-family SO(10) and E_6 grand unification models in heterotic string theory using conformal field theory and asymmetric orbifolds, identifying unique models with specific hidden sectors and anomaly-free spectra.

Contribution

It provides a comprehensive classification of 3-family GUT models in heterotic string theory based on Z_6 asymmetric orbifolds with a Z_3 automorphism, including unique models with specific hidden sectors.

Findings

Identifies a unique SO(10) model with a non-asymptotically-free hidden sector.

Classifies 17 models with SU(2) hidden sectors and specific chiral spectra.

Finds a unique E_6 model with an asymptotically-free SU(2) hidden sector.

Abstract

We give a classification of 3-family SO(10) and E_6 grand unification in string theory within the framework of conformal field theory and asymmetric orbifolds. We argue that the construction of such models in the heterotic string theory requires certain Z_6 asymmetric orbifolds that include a Z_3 outer-automorphism, the latter yielding a level-3 current algebra for the grand unification gauge group SO(10) or E_6. We then classify all such Z_6 asymmetric orbifolds that result in models with a non-abelian hidden sector. All models classified in this paper have only one adjoint (but no other higher representation) Higgs field in the grand unified gauge group. In addition, all of them are completely anomaly free. There are two types of such 3-family models. The first type consists of the unique SO(10) model with SU(2) X SU(2) X SU(2) as its hidden sector (which is not asymptotically-free at the string scale). This SO(10) model has 4 left-handed and 1 right-handed 16s. The second type is described by a moduli space containing 17 models (distinguished by their massless spectra). All these models have an SU(2) hidden sector, and 5 left-handed and 2 right-handed families in the grand unified gauge group. One of these models is the unique E_6 model with an asymptotically-free SU(2) hidden sector. The others are SO(10) models, 8 of them with an asymptotically free hidden sector at the string scale.