Heterotic free fermionic and symmetric toroidal orbifold models

TL;DR

This paper establishes a detailed correspondence between free fermionic models and symmetric heterotic toroidal orbifolds, clarifying their equivalence and translating key data between the two frameworks for Z2xZ2 orbifolds.

Contribution

It provides the first comprehensive dictionary relating free fermionic input data to orbifold phases, including explicit realizations for all six-dimensional Z2xZ2 orbifolds.

Findings

Generalized GSO phases correspond to torsion phases in orbifolds

Explicit translation methods between models are developed

All six-dimensional Z2xZ2 orbifold geometries are realized in free fermionic form

Abstract

Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for Z2xZ2 orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: We give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all Z2xZ2 orbifold geometries in six dimensions.