# Classification of symmetric toroidal orbifolds

@article{Fischer2013ClassificationOS,
title={Classification of symmetric toroidal orbifolds},
author={Maximilian Fischer and Michael Ratz and Jes'us Torrado and Patrick K. S. Vaudrevange},
journal={Journal of High Energy Physics},
year={2013},
volume={2013},
pages={1-53}
}
• Published 18 September 2012
• Mathematics
• Journal of High Energy Physics
A bstractWe provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield $\mathcal{N}\geq 1$ supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six dimensions. We find in total 520 inequivalent toroidal orbifolds, 162 of them with Abelian point groups such as ${{\mathbb{Z}}_3},{{\mathbb{Z}}_4},{{\mathbb{Z}}_6}\hbox{-}\mathrm{I}$ etc. and 358 with non-Abelian point groups such as S3, D4…

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