Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Li\'enard-Wiechert fields

TL;DR

This paper explores how flat space scattering amplitudes emerge from AdS/CFT by analyzing geodesics and Lif3nard-Wiechert fields, revealing antipodal matching in the flat limit.

Contribution

It demonstrates the construction of flat space scattering amplitudes from AdS geodesics and shows antipodal matching of Lif3nard-Wiechert solutions in the flat limit.

Findings

Flat space amplitudes can be derived from AdS geodesic operator insertions.

Lif3nard-Wiechert solutions in AdS exhibit antipodal matching.

Antipodal matching in AdS leads to flat space antipodal matching at infinity.

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 Li\'enard-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.