20378 2206.10547 10.1007/JHEP03(2023)030 30 30 Eikonal approximation in celestial CFT Regular Article - Theoretical Physics 1 39 2023 3 6 2022 12 5 2023 2 15 2023 3 6 The Author(s) 2023 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2023 2023 3 3 Leonardo Pipolo de Gioia pipolo@ifi.unicamp.br Ana-Maria Raclariu a.m.raclariu@uva.nl grid.411087.b 0000 0001 0723 2494 University of Campinas — UNICAMP, Institute of Physics “Gleb-Wataghin” Campinas SP 13083-859 Brazil grid.420198.6 0000 0000 8658 0851 Perimeter Institute for Theoretical Physics 31 Caroline St. N Waterloo N2L 2Y5 Canada grid.7177.6 0000000084992262 Universiteit van Amsterdam Science Park 904 1098 XH Amsterdam the Netherlands Abstract We identify an eikonal regime in celestial CFT2 in which massless 2-2 scattering is dominated by t-channel exchange. We derive a formula for the celestial amplitude that resums exchanges of arbitrary integer spin to all orders in the coupling. The resulting eikonal phase takes the same form as in flat space with the powers of center-of-mass energy replaced by weight-shifting operators on the celestial sphere. We independently compute the celestial two-point function for a scalar propagating in a shockwave background and show that to leading order in the gravitational coupling and for a suitable choice of the source, the result agrees with the prediction from the celestial eikonal formula for graviton exchange. We demonstrate that this two-point function can be directly obtained from the corresponding formula in AdS4 in a flat space limit. We finally establish a general relation between scalar celestial amplitudes in celestial CFT d−1 and the flat space limit of scalar AdS d+1 Witten diagrams. Keywords AdS-CFT Correspondence Nonperturbative Effects Scattering Amplitudes ArXiv ePrint: 2206.10547