Application of the Weinberg's conditions of asymptotic safety to amplitudes and not to couplings of the effective action can help to uniquely define the running in the UV and avoid some of the asymptotic safety program problems. As it turns out the requirement for a quantum gravity to be defined by S-matrix, that obeys the Weinbergs asymptotic safety criteria is a very restrictive one. The idea is illustrated by the 4-graviton amplitude in string theory and its symmetries.

中文翻译：

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渐近安全性和量子引力振幅

将Weinberg渐近安全条件应用于振幅而非有效作用的耦合，可以帮助唯一定义UV中的运行并避免一些渐进安全程序问题。事实证明，由S矩阵定义量子引力的要求非常严格，它遵循了Weinbergs渐近安全标准。弦论中的4重音振幅及其对称性说明了这一思想。