Classification of the Chiral Z2 x Z2 Heterotic String Models
Abstract
This thesis provides a classification of the chiral content of the heterotic Z2 × Z2 orbifold models. We show that the chiral content of the heterotic Z2 × Z2 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 Z2 × Z2 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 Z2 fermionic projections. In this class of vacua the chiral content of the models is determined by the underlying N = 4 mother theory.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.