| Summary: | Abstract Carrollian conformal field theories (carrollian CFTs) are natural field theories on null infinity of an asymptotically flat spacetime or, more generally, 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(1, 3), 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.
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