Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude

TL;DR

This paper investigates constraints on higher-dimension operators in four-graviton scattering amplitudes, revealing that consistent effective theories occupy small parameter regions and are more constrained than previously thought.

Contribution

It introduces new bounds on gravitational EFT coefficients using unitarity, crossing symmetry, and amplitude methods, and identifies small allowed parameter islands from string and field theory amplitudes.

Findings

EFT coefficients lie in small constrained islands.

Leading coefficients can be derived from dispersive representations.

Weakly-coupled gravitational theories are more constrained than dispersive bounds suggest.

Abstract

We analyze constraints from perturbative unitarity and crossing on the leading contributions of higher-dimension operators to the four-graviton amplitude in four spacetime dimensions, including constraints that follow from distinct helicity configurations. We focus on the leading-order effect due to exchange by massive degrees of freedom which makes the amplitudes of interest infrared finite. In particular, we place a bound on the coefficient of the $R^3$ operator that corrects the graviton three-point amplitude in terms of the $R^4$ coefficient. To test the constraints we obtain nontrivial effective field-theory data by computing and taking the large-mass expansion of the one-loop minimally-coupled four-graviton amplitude with massive particles up to spin 2 circulating in the loop. Remarkably, we observe that the leading EFT coefficients obtained from both string and one-loop field-theory amplitudes lie in small islands. The shape and location of the islands can be derived from the dispersive representation for the Wilson coefficients using crossing and assuming that the lowest-spin spectral densities are the largest. Our analysis suggests that the Wilson coefficients of weakly-coupled gravitational physical theories are much more constrained than indicated by bounds arising from dispersive considerations of $2 \to 2$ scattering. The one-loop four-graviton amplitudes used to obtain the EFT data are computed using modern amplitude methods, including generalized unitarity, supersymmetric decompositions and the double copy.