Flat-Space, BMS, and Celestial Holography

Flat-space holography starts from unusually sharp observables—radiative data at null infinity, asymptotic charges, memory, and the gravitational S-matrix—but lacks the timelike conformal boundary that organizes AdS/CFT. Celestial amplitudes reorganize scattering data through a definite integral transform Pasterski 2021; that fact alone does not provide a complete boundary theory. This chapter explains what BMS, celestial, and Carrollian constructions already determine and which additional ingredients a unitary boundary dual would require.

Helpful background. S-Matrix and T-Matrix Normalization fixes scattering conventions; Soft Theorems supplies the infrared Ward identities; Celestial Amplitudes supplies the transform as an amplitude object; AdS Wavepackets and Boundary Extraction of Flat-Space Scattering provides one controlled route from a known holographic dictionary; and de Sitter Holography: Dictionary Completeness, Obstructions, and Status offers a useful non-AdS comparison.

The asymptotic-data problem

In four-dimensional asymptotically flat gravity, future and past null infinity carry radiative phase spaces. The Bondi news records gravitational radiation, constraint equations connect it to Coulombic charges, and matching conditions can relate incoming to outgoing data. These structures are necessary for scattering. They do not alone specify a lower-dimensional quantum theory with a Hilbert space, operator algebra, dynamics, positive inner product, and an inverse map for all bulk observables.

Three reorganizations recur throughout the chapter:

• BMS and soft data relate asymptotic charges, soft insertions, and memory under declared falloffs and matching conditions.
• Celestial data Mellin-transform external energies so four-dimensional Lorentz symmetry acts as two-dimensional conformal symmetry on the celestial sphere.
• Carrollian data retain retarded time on null infinity and organize flux-balance laws in a field theory on a degenerate boundary geometry.

Each has exact or perturbatively controlled components. The central discipline is to distinguish those results from the stronger claim that one construction defines all of quantum gravity in flat spacetime.

A route through the chapter

1. Flat-Space Holography and Asymptotic Observables defines the possible targets and the evidence needed to go beyond an S-matrix rewrite.
2. Null-Infinity Radiative Data as Candidate Boundary Data separates radiative, Coulombic, charge, and corner information.
3. BMS, Memory, and Soft Sectors as Holographic Data derives the leading symmetry–soft–memory relation and its boundary assumptions.
4. Infrared-Dressed Scattering States and Boundary Dictionaries replaces bare Fock states by infrared-finite observables and charged sectors.
5. AdS Flat Limits as Candidate Flat-Holography Dictionaries extracts scattering from AdS correlators without assuming a standalone flat dual.
6. Celestial CFT and Scattering Interfaces identifies exactly what the Mellin transform establishes.
7. Celestial Bases and Boost Eigenstates as Boundary-Dictionary Inputs proves normalization and inversion on the appropriate principal series.
8. Celestial OPEs, Loop Corrections, and Infrared Factorization follows collinear and soft structures beyond tree level.
9. Carrollian and Other Flat-Boundary Holography Proposals: Evidence and Obstructions compares null-boundary currents with full radiative data.
10. Flat and Celestial Dictionaries: Unitarity, Completeness, and Status applies one set of completion tests to the proposals.

Five non-equivalences to retain

An infrared-divergent Fock-space matrix element is not an exact gravitational S-matrix. An infrared-finite dressed S-matrix is not the whole algebra of asymptotic observables. An invertible Mellin transform of that S-matrix is not, merely by covariance, a local Euclidean CFT. Ward identities of a sourced Carrollian theory are not an inverse reconstruction theorem. Finally, deriving a flat S-matrix from an AdS/CFT pair does not construct a boundary theory intrinsic to Minkowski null infinity.

These distinctions are productive: they show precisely what has been achieved and turn “flat holography” into a sequence of falsifiable questions about states, observables, dynamics, infrared sectors, and completeness.

Review the chapter

You should be able to integrate a Bondi constraint across a radiation burst, derive the leading BMS Ward identity, explain how dressing changes the asymptotic Hilbert space, construct and invert a celestial primary basis, and track how an infrared logarithm modifies celestial operator data. Given any flat-boundary proposal, you should be able to ask for its inner product, massive states, loop prescription, reconstruction map, fixed-theory factorization, and nonperturbative definition.

The literature boundary used for frontier statements in this chapter is 10 August 2026. Later claims belong in a dated research assessment rather than being silently folded into these stable distinctions.

Chapter-scale structure and validity checks

The chapter-scale structure map locates this page’s result inside the full reasoning chain. Follow the solid arrows through the declared inputs and checks; the dashed final arrow marks the point where an additional inference would be required.

A flat-space S-matrix, its celestial transform, BMS charges, and a complete celestial dual are distinct layers of a proposed dictionary. The diagram is an original schematic, is not to scale, and uses the dashed final arrow to mark the claim boundary.

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The companion validity map turns three common overclaims into explicit failure tests. Read each row from its declared object to the diagnostic, then compare the licensed conclusion with the dashed “not” endpoint.

A flat-space S-matrix, its celestial transform, BMS charges, and a complete celestial dual are distinct layers of a proposed dictionary. Each row pairs a diagnostic with the strongest supported conclusion and an explicitly unsupported promotion. The diagram is an original schematic and is not to scale.

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Claim-domain comparison

The table below gives a screen-reader-friendly comparison of three representative claims. It keeps the required declaration, approximation status, evidence timing, counterevidence, falsifier, failure condition, and licensed conclusion in one reading order.

Representative claim domains and validity boundaries for Flat-Space, BMS, and Celestial Holography

Claim object	State, ensemble, and conventions	Approximation, status, and evidence timing	Uncertainty and counterevidence	Falsifier	Failure condition	Licensed conclusion
asymptotic symmetry	Declare falloffs, charges, and phase space; use the volume conventions unless the page states a local replacement.	Conditional theorem or structural result. Control chain: null-infinity states and data → BMS, soft, and dressing sectors → celestial transform and OPE → loop, unitarity, and completeness tests → flat-holography status. Sources are cited on the destination page; literature checked through 10 August 2026.	Track omitted corrections, alternate branches, and competing definitions. A failed “soft theorem and memory triangle” check is counterevidence to the promoted claim.	soft theorem and memory triangle	a complete holographic dual	a Ward identity for scattering data
celestial transform	Declare basis, contour, and infrared dressing; use the volume conventions unless the page states a local replacement.	Proposal or conditional construction. Control chain: null-infinity states and data → BMS, soft, and dressing sectors → celestial transform and OPE → loop, unitarity, and completeness tests → flat-holography status. Sources are cited on the destination page; literature checked through 10 August 2026.	Track omitted corrections, alternate branches, and competing definitions. A failed “inverse transform and covariance” check is counterevidence to the promoted claim.	inverse transform and covariance	a standalone local CFT	repackaged S-matrix data
celestial OPE	Declare operator basis, loop order, and regulator; use the volume conventions unless the page states a local replacement.	Proposal or conditional construction. Control chain: null-infinity states and data → BMS, soft, and dressing sectors → celestial transform and OPE → loop, unitarity, and completeness tests → flat-holography status. Sources are cited on the destination page; literature checked through 10 August 2026.	Track omitted corrections, alternate branches, and competing definitions. A failed “factorization and unitarity checks” check is counterevidence to the promoted claim.	factorization and unitarity checks	nonperturbative completeness	an OPE-like organization in its domain

Download the structured table data (JSON).

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.