Differential Representation for Carrollian Correlators

Abstract: The differential representation of AdS correlators offers a framework to express exchange Witten diagrams as functions of non-local differential operators applied to contact Witten diagrams. In this paper, we develop the differential representation for scalar Carrollian correlators. We first construct this representation using the recently formulated Carrollian limit of AdS Witten diagrams. We then provide an alternate intrinsic analysis that leverages the properties of the Carrollian bulk-to-boundary propagator. Using the differential representation, we also obtain differential Bern-Carrasco-Johansson (BCJ) relations for Carrollian correlators.