Carrollian and Other Flat-Boundary Holography Proposals: Evidence and Obstructions

Null infinity carries a Carrollian geometry: its induced metric is degenerate along the null generators, and the BMS group acts as a conformal Carrollian symmetry. This makes a Carrollian field theory a natural candidate language for flat holography. Existing constructions reproduce important flux-balance and celestial Ward identities, but an intrinsic boundary dynamics and complete inverse map remain separate requirements.

Required background. Null-Infinity Radiative Data as Candidate Boundary Data supplies the target phase space, and Evidence Programs for Holographic Duality supplies the standard for turning a matching calculation into a duality claim.

Helpful background. BMS, Memory, and Soft Sectors as Holographic Data supplies flux Ward identities, while Celestial and Cosmological Correlators: Axiom and Handoff Audit supplies the comparison with conformal correlators.

Carrollian geometry at null infinity

A Carrollian structure consists schematically of a degenerate spatial metric $q_{ab}$ and a preferred vector $n^a$ satisfying

$$q_{ab}n^b=0.$$

At $\mathscr I^+$, $n=\partial_u$ runs along the null generators and $q_{AB}$ is the sphere metric on cuts. Transformations preserving this structure up to conformal rescaling generate BMS-type symmetries. This geometric identification is precise and independent of whether a quantum dual exists; its relation to BMS symmetry is developed in Duval, Gibbons, and Horváthy 2014.

A sourced Carrollian theory can couple its boundary fields to the Bondi shear and other asymptotic data. Radiation then appears as a source of nonconservation rather than as a contradiction to boundary dynamics. Schematically,

$$\partial_u\mathcal E+D_A\mathcal P^A =\mathcal S^{AB}N_{AB}+\text{matter sources},$$

where the precise response $\mathcal S^{AB}$ and signs depend on the source convention. Suitable moments reproduce BMS flux-balance laws. Donnay et al. 2023, §§3–5 also exhibit an integral transform connecting these Carrollian Ward identities to celestial ones.

Mapping a radiative observable

For a compact burst, the weighted asymptotic flux

$$\Delta Q_f =\int du\,d^2\Omega\;f(x^A) \left(\frac{1}{32\pi G}N_{AB}N^{AB} +T_{uu}^{\rm matter}\right)$$

can be represented as the change of a Carrollian charge sourced by radiation. This maps a well-defined bulk observable to boundary current data. Reconstruction of the full news would require the time-resolved response and its phase information, not merely the integrated charge.

First application. Map a simple radiative phase-space observable into a proposed Carrollian boundary stress-tensor or current datum and list the inverse information required for reconstruction. Use one news profile, derive its flux moment and sourced Ward identity, then state whether the boundary data determine $N_{AB}(u,x)$, its polarization, Coulombic integration constants, and the incoming state.

Evidence and obstructions

The sourced conformal Carrollian construction reproduces kinematic symmetries and flux laws, and explicit free Carrollian theories provide useful models. These are substantive results. They do not select a unique interacting theory for four-dimensional Einstein gravity, include all massive sectors at timelike infinity, or establish a positive fixed-theory Hilbert space. The 2026 review by Ruzziconi, §§5–7 presents these advances together with the remaining open directions.

Adversarial control. Choose two news waveforms with the same total weighted energy flux but different time dependence or polarization. They give the same selected integrated current while defining different radiative scattering data. Unless the proposal includes the additional local responses needed to separate them, that current map is noninjective and cannot be called complete reconstruction.

Evidence ceiling

Carrollian geometry, BMS covariance, and matched Ward identities give a well-motivated boundary framework. As of 10 August 2026 they support concrete sectors of a flat-space dictionary, not a general nonperturbative dual with complete states, observables, dynamics, and inverse reconstruction.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Donnay, Laura, Adrien Fiorucci, Yannick Herfray, and Romain Ruzziconi. “Bridging Carrollian and Celestial Holography.” Physical Review D 107 (2023): 126027. DOI; Open PDF.
• Donnay, Laura, Adrien Fiorucci, Yannick Herfray, and Romain Ruzziconi. “Carrollian Perspective on Celestial Holography.” Physical Review Letters 129 (2022): 071602. DOI; Open PDF.
• Duval, Christian, Gary W. Gibbons, and Peter A. Horváthy. “Conformal Carroll Groups and BMS Symmetry.” Classical and Quantum Gravity 31 (2014): 092001. DOI; Open PDF.
• Ruzziconi, Romain. “Carrollian Physics and Holography.” (2026). arXiv:2602.02644.