A Classification of 3-Family Grand Unification in String Theory II. The SU(5) and SU(6) Models

TL;DR

This paper classifies string theory models with three chiral families based on supersymmetric SU(5) and SU(6) grand unification, constructed via asymmetric orbifolds, identifying possible hidden sectors and Higgs fields.

Contribution

It provides a comprehensive classification of Z_6 asymmetric orbifold models with three families, including hidden sectors and Higgs content, within heterotic string theory.

Findings

All models have one adjoint Higgs field neutral under other symmetries.

Hidden sectors include SU(2), SU(3), and SU(2)×SU(2) for SU(6) models.

Some models feature an anomalous U(1).

Abstract

Requiring that supersymmetric SU(5) and SU(6) grand unifications in the heterotic string theory must have 3 chiral families, adjoint (or higher representation) Higgs fields in the grand unifiedgauge group, and a non-abelian hidden sector, we construct such string models within the framework of conformal field theory and asymmetric orbifolds. Within this framework, we construct all such string models via 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 SU(5) or SU(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 otherhigher representation) Higgs field in the grand unified gauge group. This Higgs field is neutral under all other gauge symmetries. The list of hidden sectors for 3-family SU(6) string models are SU(2), SU(3) and $SU(2) \otimes SU(2)$. In addition to these, 3-family SU(5) string models can also have an SU(4) hidden sector. Some of the models have an anomalous U(1).