Gravity and a universal cutoff for field theory

Abstract

We analyze the one-loop effects of massive fields on 2-to-2 scattering processes involving gravitons. It has been suggested that in the presence of gravity, any local effective field theory description must break down at the "species scale". We first observe that unitarity and analyticity of the amplitude indeed imply a species-type bound $GΛ^{d-2}N\leq O(1)$, where $N$ counts parametrically light species and $Λ$ is an energy scale above which new unknown ingredients must modify the graviton amplitude. To clarify what happens at this scale, we contrast the partial wave decomposition of calculated amplitudes with that of some ultraviolet scenarios: string theory and strongly interacting Planck-scale physics. Observing that the latter exhibit a markedly stronger high-spin content, we define nonperturbatively the high-spin onset scale $Λ_{\rm o}$, which coincides with the string scale and higher-dimensional Planck scale in respective examples. We argue that, generally, no local field description can exist at distances shorter than $1/Λ_{\rm o}$.