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Abstract
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.
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