# T-duality orbifolds of heterotic Narain compactifications

## TL;DR

This paper develops a unified framework for symmetric and asymmetric heterotic orbifolds by systematically studying Narain compactifications orbifolded by T-duality groups, introducing new classification tools and examples.

## Contribution

It generalizes the space group description to Narain orbifolds, introduces a character formula for moduli counting, and develops machinery for classifying Narain orbifolds.

## Key findings

- Unified crystallographic description of Narain orbifolds
- Derived a character formula for unfixed moduli
- Presented new examples including T-folds

## Abstract

To obtain a unified framework for symmetric and asymmetric heterotic orbifold constructions we provide a systematic study of Narain compactifications orbifolded by finite order T-duality subgroups. We review the generalized vielbein that parametrizes the Narain moduli space (i.e. the metric, the B-field and the Wilson lines) and introduce a convenient basis of generators of the heterotic T-duality group. Using this we generalize the space group description of orbifolds to Narain orbifolds. This yields a unified, crystallographic description of the orbifold twists, shifts as well as Narain moduli. In particular, we derive a character formula that counts the number of unfixed Narain moduli after orbifolding. Moreover, we develop new machinery that may ultimately open up the possibility for a full classification of Narain orbifolds. This is done by generalizing the geometrical concepts of Q-, Z- and affine classes from the theory of crystallography to the Narain case. Finally, we give a variety of examples illustrating various aspects of Narain orbifolds, including novel T-folds.

---
Source: https://tomesphere.com/paper/1703.05323