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Résumé |
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 R3 operator that corrects the graviton three-point amplitude in terms of the R4
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→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. |
