Flat-Space, BMS, and Celestial Holography
Flat-space holography organizes gravitational scattering through null-infinity data, asymptotic symmetries, and celestial or Carrollian variables. This chapter explains these concrete dictionaries while separating a change of scattering basis from a complete boundary quantum theory.
Enter this chapter
Section titled “Enter this chapter”Begin with Flat-Space Holography and Asymptotic Observables to choose whether the target is scattering, radiative data, or an asymptotic observable algebra.
Helpful background. S-Matrix and T-Matrix Normalization and Soft Theorems supply scattering normalization and infrared factorization.
Topics
Section titled “Topics”- Flat-Space Holography and Asymptotic Observables — Defines the observables a flat-boundary proposal aims to encode.
- Null-Infinity Radiative Data as Candidate Boundary Data — Separates radiative modes from constrained charges and corner data.
- BMS, Memory, and Soft Sectors as Holographic Data — Connects leading soft identities, asymptotic symmetry, and gravitational memory.
- Infrared-Dressed Scattering States and Boundary Dictionaries — Explains why long-range fields change the asymptotic state space.
- AdS Flat Limits as Candidate Flat-Holography Dictionaries — Extracts localized flat-space scattering from a controlled AdS limit.
- Celestial CFT and Scattering Interfaces — Reexpresses amplitudes in variables with celestial conformal covariance.
- Celestial Bases and Boost Eigenstates as Boundary-Dictionary Inputs — Constructs boost eigenstates and states the domain of inversion.
- Celestial OPEs, Loop Corrections, and Infrared Factorization — Tracks soft and collinear structures through loop corrections.
- Carrollian and Other Flat-Boundary Holography Proposals: Evidence and Obstructions — Examines null-boundary geometries and candidate intrinsic dynamics.
- Flat and Celestial Dictionaries: Unitarity, Completeness, and Status — Tests the remaining inner-product, infrared, and reconstruction requirements.
How the ideas fit together
Section titled “How the ideas fit together”A Mellin transform of external energies converts Lorentz covariance into conformal covariance on the celestial sphere. On a domain where the transform is invertible, it preserves the scattering information; it does not create new dynamics. The conformal-primary construction makes this distinction explicit Pasterski 2021, § 4.1. Meanwhile, soft charges and memory constrain which asymptotic sectors the amplitudes connect. A complete dictionary must reconcile both ingredients with infrared-finite observables and a physical inner product; covariance or a tree-level operator product alone cannot supply them.
Claim-domain comparison
Section titled “Claim-domain comparison”Compare the assumptions and strongest supported conclusion for each case.
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| 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. | Under the stated falloffs and infrared prescription, the charge-flux Ward identity disagrees with the corresponding soft scattering relation. | Promoting an asymptotic Ward identity to 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. | Within the declared transform domain, the inverse fails to recover the original dressed amplitude or the predicted covariance fails. | Identifying transformed S-matrix data with 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. | At the stated loop order and regulator, the proposed coefficients fail to reproduce the required collinear factorization residue. | Promoting an OPE-like expansion in a controlled domain to nonperturbative completeness. | an OPE-like organization in its domain |
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Where to go next
Section titled “Where to go next”Continue to Quantum-Gravity Consistency and Swampland to study broader restrictions on possible gravitational theories and the hypotheses behind them.