Carrollian Amplitudes from Holographic Correlators

TL;DR

This paper demonstrates that Carrollian amplitudes, expressed as correlators at null infinity, naturally emerge from the flat space limit of AdS boundary correlators, revealing their structure through holographic and Carrollian limits.

Contribution

It establishes a systematic connection between flat space amplitudes and AdS boundary correlators via a Carrollian limit in position space, clarifying their holographic origin.

Findings

Carrollian amplitudes are the flat space limit of AdS correlators.

Flat limit of Witten diagrams corresponds to flat space Feynman diagrams.

Distributional features and singularities of Carrollian amplitudes are explained.

Abstract

Carrollian amplitudes are flat space amplitudes written in position space at null infinity which can be re-interpreted as correlators in a putative dual Carrollian CFT. We argue that these amplitudes are the natural objects obtained in the flat space limit of AdS Lorentzian boundary correlators. The flat limit is taken entirely in position space by introducing Bondi coordinates in the bulk. From the bulk perspective, this procedure makes it manifest that the flat limit of any Witten diagram is the corresponding flat space Feynman diagram. It also makes explicit the fact that the flat limit in the bulk is implemented by a Carrollian limit at the boundary. We systematically analyse tree-level two, three and four-point correlators. Familiar features such as the distributional nature of Carrollian amplitudes and the presence of a bulk point singularity arise naturally as a consequence of requiring a finite and non-trivial Carrollian limit.