Classification of symmetric toroidal orbifolds

TL;DR

This paper systematically classifies six-dimensional symmetric toroidal orbifolds that preserve N≥1 supersymmetry in four dimensions, identifying 520 inequivalent cases with detailed properties.

Contribution

It provides the first complete classification of such orbifolds based on six-dimensional crystallographic space groups, including analysis of their gauge symmetry breaking mechanisms.

Findings

Identified 520 inequivalent orbifolds with various point groups.

Detailed properties of orbifolds with Abelian point groups, including Hodge numbers.

Discussion on mechanisms of gauge symmetry breaking.

Abstract

We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N>=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 Z_3, Z_4, Z_6-I etc. and 358 with non-Abelian point groups such as S_3, D_4, A_4 etc. We also briefly explore the properties of some orbifolds with Abelian point groups and N=1, i.e. specify the Hodge numbers and comment on the possible mechanisms (local or non-local) of gauge symmetry breaking.