The isomorphism between the BMS4 algebra and the 3D Carrollian conformal algebra hints towards a co-dimension one formalism of at holography with the field theory residing on the null-boundary of the asymptotically at space-time enjoying a 3D Carrollian conformal symmetry. Motivated by this fact, I shall first discuss the general symmetry properties of a 3D Carrollian CFT, adopting a purely intrinsic, field-theoretic approach. I shall then demonstrate how the 4D bulk leading and sub-leading soft graviton theorems arise directly from the position-space Ward identities of the Carrollian Stress-tensor. Finally, I shall discuss how to intrinsically encode the infinite tower of the tree-level bulk soft graviton theorems into the 3D Carrollian CFT.
(Based on 2304.02696, 2308.03673 and ongoing work with R. Ruzziconi)