Is 4D flat-space gravity dual to a 3D Carrollian field theory
In plain words
An alternative to the celestial sphere places the equivalent description of flat-space gravity on null infinity, the surface reached by outgoing light rays, as a theory in which the speed of light is effectively zero (a Carrollian theory). Whether such a theory exists with its own rules, independent of the gravity calculation, is unknown.
Precise statement
Carrollian holography proposes that the 4D asymptotically flat gravitational S-matrix equals correlators of a sourced 3D conformal Carrollian field theory on null infinity, constrained by BMS Ward identities (Donnay, Fiorucci, Herfray, Ruzziconi 2022). Determine whether an intrinsically defined Carrollian theory exists whose correlators reproduce tree and one-loop graviton amplitudes, and how it relates to the celestial CFT.
What would settle it
An intrinsic 3D Carrollian theory whose correlators are computed without reference to the bulk and match 4D graviton amplitudes through one loop, or a proof that no local Carrollian theory can do so.
Status in the literature
The framework and its Ward identities were set up in 2022; no intrinsic dual of Einstein gravity is known.