# Nonexistence of locally but not globally supersymmetric orbifolds

## TL;DR

This paper proves that in heterotic string theory, orbifolds that are locally but not globally supersymmetric cannot have a vanishing one-loop partition function, indicating such configurations do not exist.

## Contribution

The paper provides a nonexistence proof showing that orbifolds with local but not global supersymmetry cannot have zero one-loop heterotic string partition functions.

## Key findings

- Such orbifolds do not exist.
- Representation theory rules out local but not global supersymmetry.
- No vanishing partition function for these orbifolds.

## Abstract

Motivated by the smallness of the cosmological constant we investigate whether it is possible to have vanishing one-loop heterotic string partition functions for six-dimensional non-supersymmetric toroidal orbifolds. A straightforward way to realize this presents itself, when each orbifold sector separately preserves some Killing spinors, but none of them survives in all sectors combined. By applying some representation theory to the abstract finite point groups underlying toroidal orbifolds it turns out, that this is never possible. This leads to a nonexistence proof of locally but not globally supersymmetric orbifolds.