From AdS correlators to Carrollian amplitudes with the scattering equation

TL;DR

This paper establishes a connection between AdS boundary correlators and Carrollian scattering amplitudes using the scattering equations and ambitwistor strings, providing a new perspective on flat space limits in various dimensions.

Contribution

It proves the correspondence between AdS boundary correlators and Carrollian amplitudes via scattering equations, extending the framework to any number of external states and spacetime dimensions.

Findings

Derived Carrollian scattering equations in Minkowski space.

Reconstructed Carrollian amplitudes from AdS boundary correlators.

Commented on flat space limits of spinning correlators in AdS3.

Abstract

The scattering equations relate massless scattering kinematics to marked points on a Riemann sphere, and underpin remarkable formulae for the full tree-level S-matrices of many interesting QFTs, including cubic biadjoint scalars, Yang-Mills theory and general relativity. The scattering equations arise from worldsheet correlators of ambitwistor string theories, which has enabled their generalisation to anti-de Sitter (AdS) space in certain cases. In this paper, we use the scattering equations and ambitwistor strings to prove the correspondence between an appropriate flat limit of boundary correlators in AdS and Carrollian scattering amplitudes -- massless amplitudes written in position space on the null conformal boundary -- for any number of external states and spacetime dimensions in tree-level, cubic scalar theories. We first derive the Carrollian version of the scattering equations in Minkowski space and their associated Carrollian amplitude formulae, by direct Fourier transform from momentum space and from ambitwistor strings with a Carrollian basis of vertex operators. We then take the flat limit of known formulae for all tree-level boundary correlators of cubic scalar theories in AdS, recovering the Carrollian amplitudes in flat space. In the special case of AdS$_3$, we also make some comments on the flat space limit of spinning boundary correlators.