  Four-dimensional (4D) flat Minkowski space admits a foliation by hyperbolic
slices. Euclidean AdS3 slices fill the past and future lightcones of the
origin, while dS3 slices fill the region outside the lightcone. The resulting
link between 4D asymptotically flat quantum gravity and AdS3/CFT2 is explored
in this paper. The 4D superrotations in the extended BMS4 group are found to
act as the familiar conformal transformations on the 3D hyperbolic slices,
mapping each slice to itself. The associated 4D superrotation charge is
constructed in the covariant phase space formalism. The soft part gives the 2D
stress tensor, which acts on the celestial sphere at the boundary of the
hyperbolic slices, and is shown to be an uplift to 4D of the familiar 3D
holographic AdS3 stress tensor. Finally, we find that 4D quantum gravity
contains an unexpected second, conformally soft, dimension (2, 0) mode that is
symplectically paired with the celestial stress tensor.
