From AdS correlators to Carrollian amplitudes with the scattering equation

TL;DR

This work establishes a precise, all-m multiplicity bridge between AdS boundary correlators for cubic scalar theories and flat-space Carrollian amplitudes by employing scattering equations and ambitwistor-string methods. It derives Carrollian scattering equations in Minkowski space via momentum-to-position Fourier transforms and shows their equivalence to ambitwistor-string constructions in a Carrollian basis, yielding Carrollian CHY formulae for massless scalars in arbitrary $D$. It then proves that the flat-space limit of AdS boundary CHY representations reproduces the Carrollian amplitudes, with AdS descendants mapped to Bondi-time derivatives of the Carrollian amplitudes; the key limit scales as $\lim_{\ell\to\infty} \ell^{n((D-2)/2-\Delta)} \mathcal{C}_n(\Delta;\ell) \propto \prod_{i=1}^n \partial_{u_i}^{\Delta-1} C_n$. The results generalize to arbitrary multiplicity and dimension for scalars, and provide initial insights for spinning cases in AdS$_3$, clarifying subtle flat-limit features. Overall, the paper solidifies a robust, coordinate-friendly link between AdS correlators and Carrollian holography, leveraging CHY techniques and ambitwistor strings to illuminate the structure of flat-space limits and potential extensions to double-copy and massive Carrollian amplitudes.

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.