| Summary: | Do gravitational interactions respect the basic principles of relativity and quantum mechanics? We show that any graviton S-matrix that satisfies these assumptions cannot significantly differ from General Relativity at low energies. We provide sharp bounds on the size of potential corrections in terms of the mass M of new higher-spin states, in spacetime dimensions D ≥ 5 where the S-matrix does not suffer from infrared ambiguities. The key novel ingredient is the full set of SO(D − 1) partial waves for this process, which we show how to efficiently compute with Young tableau manipulations. We record new bounds on the central charges of holographic conformal theories. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3. We thank Cyuan-Han Chang, Clifford Cheung, Yanky Landau, Petr Kravchuk, and Sasha Zhiboedov for discussions. D. S. D., S. C. H., and Y. Z. L. are supported by the Simons Foundation through the Simons Collaboration on the Nonperturbative Bootstrap. DSD is also supported by a DOE Early Career Award under Grant No.DE-SC0019085. S. C. H. is also supported by the Canada Research Chair program, reference number CRC-2021-0042 and the Sloan Foundation. J. P. M. is supported by the DOE under Grant No.DE-SC0011632. The computations presented here were conducted in the Resnick High Performance Computing Center, a facility supported by Resnick Sustainability Institute at the California Institute of Technology. This research was enabled in part by support provided by Calcul Québec and Compute Canada (Narval and Graham clusters).
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