An Embedding Space Approach to Carrollian CFT Correlators for Flat Space Holography

TL;DR

This paper develops an embedding space formalism for 3D carrollian CFTs, linking their correlators to Minkowski scattering amplitudes and supporting their role as duals to flat space gravity.

Contribution

It introduces a new embedding space approach for 3D carrollian CFTs and explicitly derives correlators fixed by BMS symmetries, connecting them to scattering amplitudes.

Findings

Correlators match known Minkowski scattering amplitudes.

Embedding formalism simplifies the calculation of correlators.

BMS symmetries determine the form of correlators.

Abstract

Carrollian conformal field theories (carrollian CFTs) are natural field theories on null infinity of an asymptotically flat spacetime or, in general, geometries with conformal carrollian structure. Using a basis transformation, gravitational S-matrix elements can be brought into the form of correlators of a carrollian CFT. Therefore, it has been suggested that carrollian CFTs could provide a co-dimension one dual description to gravity in asymptotically flat spacetimes. In this work, we construct an embedding space formalism for three-dimensional carrollian CFTs and use it to determine two- and three-point correlators. These correlators are fixed by the global subgroup ISO(3,1) of the carrollian conformal symmetries, i.e., the Bondi--van der Burg--Metzner--Sachs symmetries (BMS). The correlators coincide with well-known two- and three-point scattering amplitudes in Minkowski space written with respect to a basis of asymptotic position states.