We consider time-dependent orbifolds in String Theory and we show that divergences are not associated with a gravitational backreaction since they appear in the open string sector too. They are related to the non existence of the underlying effective field theory as in several cases fourth and higher order contact terms do not exist. Since contact terms may arise from the exchange of string massive states, we investigate and show that some three points amplitudes with one massive state in the open string sector are divergent on the time-dependent orbifolds. To check that divergences are associated with the existence of a discrete zero eigenvalue of the Laplacian of the subspace with vanishing volume, we construct the Generalized Null Boost Orbifold where this phenomenon can be turned on and off.

中文翻译：

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关于时间依赖的双散度的起源

我们在弦理论中考虑了与时间有关的球体，并且我们证明了发散与重力反作用无关，因为它们也出现在开放的弦区域中。它们与根本有效场论的不存在有关，因为在某些情况下不存在四阶或更高阶的接触项。由于接触项可能是由于弦质量状态的交换而产生的，因此我们进行研究并表明，在开放弦区域中，一个质量状态的三点振幅在时间依赖的球面上发散。为了检查散度是否与体积消失的子空间的Laplacian离散零特征值的存在有关，我们构造了可以打开和关闭此现象的广义Null Boost Orbifold。