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 → 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.
Highlights
Background field gaugeA nice way to understand the above supersymmetric decomposition is in terms of background field gauge [30]
V we derive two-sided bounds on Wilson coefficients that follow from a single helicity configuration that describes elastic scattering; comparing to known data from string theory and our computed one-loop amplitude, we show that the results fall into small islands
In the first part, using amplitudes methods, we obtained the one-loop four-graviton amplitude with a minimally-coupled massive particle of spin up to S = 2 circulating in the loop
Summary
Systematic bounds can be placed on possible corrections to Einstein gravity [1,2,3,4,5,6,7]. We analyze our amplitudes in the large-mass limit and match to a low-energy effective field theory In this way we systematically obtain corrections to Einstein gravity due to the presence of a heavy spinning particle. Our paper naturally consists of two parts: In the first part we explain in detail the construction of the one-loop massive amplitudes used to provide theoretical data that we interpret in the second part in terms of bounds on coefficients of gravitational EFTs. Readers who are interested in the EFT constraints can skip Sect. V we derive two-sided bounds on Wilson coefficients that follow from a single helicity configuration that describes elastic scattering; comparing to known data from string theory and our computed one-loop amplitude, we show that the results fall into small islands. In Appendix H we expand these results to high orders in the large-mass expansion
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