Tension Between a Vanishing Cosmological Constant and Non-Supersymmetric Heterotic Orbifolds

TL;DR

This paper demonstrates that in non-supersymmetric heterotic orbifolds, the cosmological constant cannot vanish perturbatively at one loop due to the unavoidable absence of Killing spinors in some sectors, indicating a fundamental tension.

Contribution

It provides a model-independent no-go theorem showing the impossibility of a vanishing one-loop cosmological constant in non-supersymmetric heterotic orbifolds based on group representation theory.

Findings

No non-supersymmetric orbifold admits a sector with Killing spinors.

The mathematical reason is linked to the representation theory of finite groups.

The conjecture applies to symmetric and asymmetric orbifolds.

Abstract

We investigate under which conditions the cosmological constant vanishes perturbatively at the one-loop level for heterotic strings on non-supersymmetric toroidal orbifolds. To obtain model-independent results, which do not rely on the gauge embedding details, we require that the right-moving fermionic partition function vanishes identically in every orbifold sector. This means that each sector preserves at least one, but not always the same Killing spinor. The existence of such Killing spinors is related to the representation theory of finite groups, i.e. of the point group that underlies the orbifold. However, by going through all inequivalent (Abelian and non-Abelian) point groups of six-dimensional toroidal orbifolds we show that this is never possible: For any non-supersymmetric orbifold there is always (at least) one sector, that does not admit any Killing spinor. The underlying mathematical reason for this no-go result is formulated in a conjecture, which we have tested by going through an even larger number of finite groups. This conjecture could be applied to situations beyond symmetric toroidal orbifolds, like asymmetric orbifolds.