Carrollian Conformal Fields and Flat Holography

Abstract

The null conformal boundary I of Minkowski spacetime M plays a special role in scattering theory, as it is the locus where massless particle states are most naturally defined. We construct quantum fields on I, which create these massless states from the vacuum and transform covariantly under Poincaré symmetries. Because the latter symmetries act as Carrollian conformal isometries of I, these quantum fields are Carrollian conformal fields. This group theoretic construction is intrinsic to I by contrast to existing treatments in the literature. However, we also show that the standard relativistic massless quantum fields in M, when pulled back to I, provide a realisation of these Carrollian conformal fields. This correspondence between bulk and boundary fields should constitute a basic entry in the dictionary of flat holography. Finally, we show that I provides a natural parametrisation of the massless particles as described by irreducible representations of the Poincaré group and that in an appropriate conjugate basis, they indeed transform like Carrollian conformal fields.