Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Liénard-Wiechert fields

Abstract

We revisit the flat limit of AdS/CFT from the point of view of geodesics in AdS. We show that the flat space scattering amplitudes can be constructed from operator insertions where the geodesics of the particles corresponding to the operators hit the conformal boundary of AdS. Further, we compute the Liénard-Wiechert solutions in AdS by boosting a static charge using AdS isometries and show that the solutions are antipodally matched between two regions, separated by a global time difference of $\Delta \tau =\pi$. Going to the boundary of AdS along null geodesics, in the flat limit, this antipodal matching leads to the flat space antipodal matching near spatial infinity.

33 pages, 7 figures, minor revision (subsection 7.2 and 7.4 added, fields are smoothly extrapolated from future null infinity to its past boundary, and from past null infinity to its future boundary, mathematically rigorous derivation from the flat limit added, references added), matched to the published version

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Cited by in corpus (3)

• Radiation in Fluid/Gravity and the Flat Limit
• A Carroll Limit of AdS/CFT: A Triality with Flat Space Holography?
• Nonperfect Carrollian Fluids Through Holography