Flat-Space Holography and Asymptotic Observables

A flat-space holographic proposal must first say what it encodes. An S-matrix, the radiative phase space at null infinity, an algebra of asymptotic charges, celestial correlators, and Carrollian correlators are related objects, but they are not interchangeable. A complete claim needs a state space and inner product, observables, dynamics, infrared completion, and an inverse map whose domain is stated.

Required background. S-Matrix and T-Matrix Normalization fixes the scattering observable, while Holographic Duality: Claims, Dictionaries, and Regimes separates a dictionary entry from a full duality claim.

Helpful background. Detector Operators and Energy Flow at Null Infinity supplies measurable asymptotic operators, and AdS Wavepackets and Boundary Extraction of Flat-Space Scattering supplies a controlled comparison.

Candidate observables and their domains

For asymptotically flat scattering, one may organize the data at several levels:

1. Dressed in- and out-states and their S-matrix elements.
2. Radiative fields on $\mathscr I^-$ and $\mathscr I^+$, supplemented by constraints, Coulombic aspects, and corner data.
3. Asymptotic charges and their flux-balance laws.
4. Mellin-transformed amplitudes in a celestial conformal basis.
5. Correlators of a proposed Carrollian theory on null infinity.

An invertible map between two entries preserves the information already present. It becomes evidence for holography only when embedded in a broader structure—for example, an intrinsic boundary dynamics, nontrivial reconstruction, or consistency conditions that determine bulk observables not supplied as input.

One useful abstract statement of a fixed-theory dictionary is

$$\bigl(\mathcal H_{\rm asym},\langle\cdot,\cdot\rangle, \mathcal A_{\rm asym},S\bigr) \longleftrightarrow \bigl(\mathcal H_{\partial},\langle\cdot,\cdot\rangle_\partial, \mathcal A_\partial,U_\partial\bigr),$$

together with a map for observables and a proof of injectivity or a precisely stated quotient. Symmetry covariance constrains this map but does not supply the missing Hilbert space or dynamics.

Classifying a gravitational scattering problem

Consider two massive bodies scattering while emitting gravitons. The hard data include incoming momenta and impact parameter; the radiative data are the Bondi news at null infinity; Coulombic data contain total energy–momentum and angular momentum aspects; dressed states specify the soft clouds; and the S-matrix relates complete incoming and outgoing sectors. A celestial transform reorganizes massless legs by boost weight. A Carrollian representation retains retarded time and treats radiative flux as sourced nonconservation.

First application. Classify an asymptotically flat four-dimensional scattering problem by its radiative data, charges, dressed states, S-matrix, and two candidate boundary representations. For each representation, state which variables are inputs, which are derived, how the infrared regulator is removed, and whether an inverse map is known.

Tests that distinguish a dual from a transform

At minimum, a complete boundary proposal should specify normalizable states, a positive physical inner product or its Lorentzian replacement, all charge sectors, massive and massless excitations, loop-level dynamics, and a reconstruction map. It should reproduce crossing and unitarity of the S-matrix without taking them as unexplained external axioms. Nonperturbatively it should say which spacetime topologies and black-hole sectors are included.

Adversarial control. Give the proposal a boundary object obtained by an invertible transform of a known S-matrix, then ask it to reconstruct an asymptotic observable not contained in that input—for example a Coulombic corner datum or an operator in another superselection sector. Failure leaves a valuable scattering representation, but it blocks the stronger inference to a complete holographic dual.

Evidence ceiling

BMS, celestial, and Carrollian constructions expose deep symmetry and factorization structures in gravitational scattering. As of the literature boundary above, they do not collectively furnish a generally accepted fixed-theory boundary Hilbert space, dynamics, and inverse reconstruction for four-dimensional quantum gravity. This statement is a missing-components diagnosis, not a claim that no completion can exist.

The celestial-amplitude construction is a transform and representation change of scattering data Pasterski 2021; a complete holographic dual would additionally need the observable algebra, inner product, dynamics, and inverse map specified here.

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

• Pasterski, Sabrina. “Lectures on Celestial Amplitudes.” The European Physical Journal C 81 (2021): 1062. DOI; Open PDF.
• Ruzziconi, Romain. “Carrollian Physics and Holography.” (2026). arXiv:2602.02644.
• Strominger, Andrew. Lectures on the Infrared Structure of Gravity and Gauge Theory. Princeton: Princeton University Press, 2018. DOI; Open PDF.