Scattering Amplitudes: Celestial and Carrollian

TL;DR

This work proposes a bridge between Celestial holography and Carrollian holography by showing that 3d Carrollian CFTs on the null boundary of 4d flat spacetime can encode 4d massless scattering amplitudes via a modified Mellin (Mellin–Fourier) framework. It identifies two branches of Carrollian correlators, with the time-dependent (delta-function) branch being the key channel for relating boundary correlators to bulk S-matrix elements, and provides an explicit massless Carroll scalar example that yields Delta = 1/2 and delta-function-type correlators consistent with the proposed connection. The central claim is formalized as a time-dependent Carrollian correlator equal to the modified Mellin amplitude, enabling a potential holographic description of flat-space scattering; however, realizing this in full requires incorporating an infinite spectrum of complex-dimension primaries and expanded asymptotic symmetries beyond standard BMS$_4$. Overall, the paper advances flat-space holography by outlining a concrete route to compute bulk amplitudes from boundary Carrollian dynamics and sets the stage for constructing explicit Carroll CFTs with the requisite symmetries.

Abstract

Recent attempts at the construction of holography for asymptotically flat spacetimes have taken two different routes. Celestial holography, involving a two dimensional (2d) CFT dual to 4d Minkowski spacetime, has generated novel results in asymptotic symmetry and scattering amplitudes. A different formulation, using Carrollian CFTs, has been principally used to provide some evidence for flat holography in lower dimensions. Understanding of flatspace scattering has been lacking in the Carroll framework. In this work, using ideas from Celestial holography, we show that 3d Carrollian CFTs living on the null boundary of 4d flatspace can potentially compute bulk scattering amplitudes. 3d Carrollian conformal correlators have two different branches, one depending on the null time direction and one independent of it. We propose that it is the time-dependent branch that is related to bulk scattering. We construct an explicit field theoretic example of a free massless Carrollian scalar that realises some desired properties.