Abstract
The requirement that particles propagate causally on non-trivial backgrounds implies interesting constraints on higher-derivative operators. This work is part of a systematic study of the positivity bounds derivable from time delays on shockwave backgrounds. First, we discuss shockwaves in field theory, which are infinitely boosted Coulomb-like field configurations. We show how a positive time delay implies positivity of four-derivative operators in scalar field theory and electromagnetism, consistent with the results derived using dispersion relations, and we comment on how additional higher-derivative operators could be included.
We then turn to gravitational shockwave backgrounds. We compute the infinite boost limit of Reissner-Nordström black holes to derive charged shockwave backgrounds. We consider photons traveling on these backgrounds and interacting through four-derivative corrections to Einstein-Maxwell theory. The inclusion of gravity introduces a logarithmic term into the time delay that interferes with the straightforward bounds derivable in pure field theory, a fact consistent with CEMZ and with recent results from dispersion relations. We discuss two ways to extract a physically meaningful quantity from the logarithmic time delay — by introducing an IR cutoff, or by considering the derivative of the time delay — and comment on the bounds implied in each case. Finally, we review a number of additional shockwave backgrounds which might be of use in future applications, including spinning shockwaves, those in higher dimensions or with a cosmological constant, and shockwaves from boosted extended objects.
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Acknowledgments
We would like to thank Simon Caron-Huot, Clifford Cheung, Tom Hartman, Johan Henriksson, Julio Parra-Martinez, Andrew Tolley and Alessandro Vichi for a number of useful conversations and correspondences. This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement no. 758903). The work of S.C. and Y.T. is supported in part by the NSF grant PHY-2210271. This work benefited greatly from participation in the program “Bootstrapping Quantum Gravity” at the Kavli Institute for Theoretical Physics at UC Santa Barbara. S.C. thanks KITP for their hospitality. This research was supported in part by grant NSF PHY-1748958 to the Kavli Institute for Theoretical Physics (KITP).
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Cremonini, S., McPeak, B. & Tang, Y. Electric shocks: bounding Einstein-Maxwell theory with time delays on boosted RN backgrounds. J. High Energ. Phys. 2024, 192 (2024). https://doi.org/10.1007/JHEP05(2024)192
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DOI: https://doi.org/10.1007/JHEP05(2024)192