Classification of the Chiral Z_2 x Z_2 Heterotic String Models

TL;DR

This thesis classifies the chiral content of heterotic Z2 x Z2 orbifold models, showing how they relate to free fermionic models and analyzing conditions for three-generation models.

Contribution

It provides a direct translation between orbifold and free fermionic formulations and explores the conditions for obtaining three-generation models.

Findings

Perturbative three-generation models are not possible with symmetric shifts.

Asymmetric shifts are necessary for three-generation models.

Chiral content is determined by the underlying N=4 theory.

Abstract

This thesis provides a classification of the chiral content of the heterotic $\mathbbm{Z}_2 \times \mathbbm{Z}_2$ orbifold models. We show that the chiral content of the heterotic $\mathbbm{Z}_2 \times \mathbbm{Z}_2$ orbifold models at any point in the moduli space can be described by a free fermionic model. We present a direct translation between the orbifold formulation and the free fermionic construction. We use the free fermionic description for the classification wherein we consider orbifolds with symmetric shifts. We show that perturbative three generation models are not obtained in the case of $\mathbbm{Z}_2 \times \mathbbm{Z}_2$ orbifolds with symmetric shifts on complex tori, and that the perturbative three generation models in this class necessarily employ an asymmetric shift. We show that the freedom in the modular invariant phases in the $N = 1$ vacua that control the chiral content, can be interpreted as vacuum expectation values of background fields of the underlying $N = 4$ theory, whose dynamical components are projected out by the $\mathbbm{Z}_2$ fermionic projections. In this class of vacua the chiral content of the models is determined by the underlying $N = 4$ mother theory.