Carrollian conformal correlators and massless scattering amplitudes

Abstract

The theory of particle scattering is concerned with transition amplitudes between states that belong to unitary representations of the Poincaré group. The latter acts as the isometry group of Minkowski spacetime 𝕄, making natural the introduction of relativistic tensor fields encoding the particles of interest. Since the Poincaré group also acts as a group of conformal isometries of null infinity ℐ, massless particles can also be very naturally encoded into Carrollian conformal fields living on ℐ. In this work we classify the two- and three-point correlation functions such Carrollian conformal fields can have in any consistent quantum theory of massless particles and arbitrary dimension. We then show that bulk correlators of massless fields in 𝕄 explicitly reduce to these Carrollian conformal correlators when evaluated on ℐ, although in the case of time-ordered bulk correlators this procedure appears singular at first sight. However we show that the Carrollian correlators of the descendant fields are perfectly regular and precisely carry the information about the corresponding S-matrix elements.

Feynman rules and loop structure of Carrollian amplitudes

“…Therefore, there is a beautiful triangle among scattering amplitude, celestial amplitude and Carrollian amplitude. The two-point Carrollian amplitudes have been derived in [23,24] and the three-point Carrollian amplitudes can also be found in [25,26]. The four-point scalar Carrollian amplitudes have been studied by modified Mellin transformation [27] and have been extended to gluons and gravitons systematically in recent article [28].…”