Abstract
We study constraints from causality and unitarity on 2 → 2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G → 0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.
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Acknowledgments
We thank Robert Brandenberger, Clifford Cheung, Cyuan-Han Chang, Jim Cline, Claudia de Rham, Yanky Landau, Dalimil Mazac, Leonardo Rastelli, Katelin Schutz, Andrew Tolley and Sasha Zhiboedov for discussions. DSD, SCH and YZL 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. SCH is also supported by the Canada Research Chair program and the Sloan Foundation. JPM 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. Some figures were made using the TikZ-Feynman package [82].
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Caron-Huot, S., Li, YZ., Parra-Martinez, J. et al. Causality constraints on corrections to Einstein gravity. J. High Energ. Phys. 2023, 122 (2023). https://doi.org/10.1007/JHEP05(2023)122
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DOI: https://doi.org/10.1007/JHEP05(2023)122