Abstract
We find that different asymptotic measurements in quantum field theory can be related to one another through new versions of crossing symmetry. Assuming analyticity, we conjecture generalized crossing relations for multi-particle processes and the corresponding paths of analytic continuation. We prove them to all multiplicity at tree-level in quantum field theory and string theory. We illustrate how to practically perform analytic continuations on loop-level examples using different methods, including unitarity cuts and differential equations. We study the extent to which anomalous thresholds away from the usual physical region can cause an analytic obstruction to crossing when massless particles are involved. In an appendix, we review and streamline historical proofs of four-particle crossing symmetry in gapped theories.
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Acknowledgments
S.C.H. and M.G.’s work is supported in parts by the National Science and Engineering Council of Canada (NSERC) and the Canada Research Chair program, reference number CRC-2022-00421. S.C.H.’s work is additionally supported by a Simons Fellowships in Theoretical Physics and by the Simons Collaboration on the Nonperturbative Bootstrap. The work of H.S.H. and S.M. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award Number DE-SC0009988. Additional funding for H.S.H. is provided by the William D. Loughlin Membership, an endowed fund of the Institute for Advanced Study (IAS). The work of S.M. is additionally supported by the Sivian Fund and the Roger Dashen Member Fund at the IAS. S.C.H. thanks the IAS for hospitality during a sabbatical semester where this work got started.
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Caron-Huot, S., Giroux, M., Hannesdottir, H.S. et al. Crossing beyond scattering amplitudes. J. High Energ. Phys. 2024, 60 (2024). https://doi.org/10.1007/JHEP04(2024)060
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DOI: https://doi.org/10.1007/JHEP04(2024)060