Gravity and a universal cutoff for field theory

TL;DR

This paper investigates the effects of massive fields on graviton scattering, establishing a universal cutoff scale linked to the species bound, and shows that local field theories break down at this high-energy scale.

Contribution

It introduces a nonperturbative high-spin onset scale that coincides with known fundamental scales like the string and Planck scales, clarifying the limits of local effective field theories.

Findings

Unitarity and analyticity imply a species bound on gravity theories.

The high-spin onset scale matches the string and Planck scales.

Local field descriptions fail below the high-spin onset scale.

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 $G\Lambda^{d-2}N\leq O(1)$, where $N$ counts parametrically light species and $\Lambda$ 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 $\Lambda_{\rm o}$, 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 $1/\Lambda_{\rm o}$.