Abstract
We use the S-matrix bootstrap to carve out the space of unitary, analytic, crossing symmetric and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the celestial sphere. In all dimensions, we find that the minimal allowed value of the Wilson coefficient α, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or M-theory. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although α has a unique value in M-theory, we found no evidence of an upper bound on α in 11D.
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Acknowledgments
We are grateful to Francesco Aprile, Nathan Berkovits, Lance Dixon, Michael Green and Simon Caron-Huot for numerous enlightening discussions. We also thank Simon for useful comments on the draft, and for pointing out the importance of a double scaling limit of large energy and spin. Research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. This work was additionally supported by grants from the Simons Foundation (PV: #488661, JP: #488649) and from FAPESP (2016/01343-7 and 2017/03303-1). The work of JP is supported by the Swiss National Science Foundation through the project 200020_197160 and through the National Centre of Competence in Research SwissMAP. AG is supported by the European Union — NextGenerationEU, under the programme Seal of Excellence@UNIPD, project acronym CluEs. This work was also supported by The Israel Science Foundation (grant number 2289/18), and in part by the National Science Foundation under Grant No. NSF PHY-1748958.
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ArXiv ePrint: 2212.00151
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Guerrieri, A., Murali, H., Penedones, J. et al. Where is M-theory in the space of scattering amplitudes?. J. High Energ. Phys. 2023, 64 (2023). https://doi.org/10.1007/JHEP06(2023)064
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DOI: https://doi.org/10.1007/JHEP06(2023)064