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.

中文翻译：

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消失的宇宙常数与非超对称异质球体之间的张力

我们研究了在哪种条件下，非超对称环形球面上的杂散弦的宇宙常数在单环水平上微扰消失。为了获得不依赖于模型嵌入细节的模型独立结果，我们要求右移的费米子分配函数在每个球面扇区均消失。这意味着每个扇区都保留至少一个但并不总是相同的Killing spinor。此类Killing旋转子的存在与有限群的表示理论有关，即有限元组下面的点群的表示理论。但是，通过遍历所有六维环形球面的不等价（阿贝尔和非阿贝尔）点组，我们证明这是不可能的：对于任何非超对称球面，总是（至少）一个扇区，那不承认有任何杀戮棘手。得出不通过结果的根本数学原因是通过一个猜想来表述的，我们已经通过更多的有限组进行了测试。该猜想可以应用于超出对称环形球面的情况，例如非对称球面。