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The theory of particle scattering is concerned with transition amplitudesbetween states that belong to unitary representations of the Poincar\'e group.The latter acts as the isometry group of Minkowski spacetime $\mathbb{M}$,making natural the introduction of relativistic tensor fields encoding theparticles of interest. Since the Poincar\'e group also acts as a group ofconformal isometries of null infinity $\mathcal{I}$, massless particles canalso be very naturally encoded into Carrollian conformal fields living on$\mathcal{I}$. In this work we classify the two- and three-point correlationfunctions such Carrollian conformal fields can have in any consistent quantumtheory of massless particles and arbitrary dimension. We then show that bulkcorrelators of massless fields in $\mathbb{M}$ explicitly reduce to theseCarrollian conformal correlators when evaluated on $\mathcal{I}$, although inthe case of time-ordered bulk correlators this procedure appears singular atfirst sight. However we show that the Carrollian correlators of the descendantfields are perfectly regular and precisely carry the information about thecorresponding S-matrix elements.

Carrollian conformal correlators and massless scattering amplitudes