Carrollian Approach to Flat Holography

The isomorphism between the BMS_4 algebra and the 3D 
Carrollian conformal algebra hints towards a co-dimensional one 
formalism of flat space holography with the field theory residing on the 
null-boundary of the asymptotically flat spacetime (AFS) enjoying a 3D 
Carrollian conformal symmetry. I shall first show how the leading and 
the subleading soft graviton theorems in 4D arise purely from the 
stress-tensor Ward identities of a generic 3D Carrollian conformal field 
theory defined intrinsically on the null-boundary of the 4D AFS, without 
appealing to the bulk gravitational physics. I shall then discuss, again 
purely from the boundary perspective, how an intrinsic 3D Carrollian 
conformal Ward identity can describe the subsubleading soft graviton 
theorem. It will turn out that an infinite 'w_{1+∞} tower' of Carrollian 
conformal primary fields, corresponding to an infinity of 
positive-helicity (projected) soft graviton theorems, must automatically 
exist in the theory if the OPEs are to be consistent. Finally, using the 
correspondence between the momentum-space massless scattering amplitudes 
in the 4D AFS and the 3D position-space Carrollian conformal 
correlators, I point out that those w_{1+∞} currents' OPEs with a 
primary field collectively encode the universal leading holomorphic 
collinear splitting behavior of the 4D Einstein-Yang-Mills amplitudes 
involving a positive-helicity graviton.