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REVIEW 3 major objections 6 minor 76 references

Higher-spin charges and the $L_{\Lambda} w_{1 + \infty}$ algebra in (A)dS$_4$

T0 review · 3 major / 6 minor · reviewed 2026-08-27 · deepseek-v4-flash

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Pith's one-line read An infinite tower of higher-spin charges built from the asymptotic Einstein equations makes asymptotically (A)dS$_4$ gravity canonically realize the $\Lambda$-deformed $w_{1+\infty}$ algebra on a restricted radiative phase space.

desk verdict Plausible and likely correct extension of flat-space higher-spin charges to (A)dS4, but the letter leans on a companion paper and one load-bearing assumption about the recursion at all spins. read the letter →

arxiv 2608.22625 v1 pith:METWGN7F submitted 2026-08-23 hep-th

Lorenzo Di Giacomo , Maitá Micol , Daniele Pranzetti , Ana-Maria Raclariu This is my paper · ORCID
classification hep-th
keywords higher-spinchargesasymptoticsymmetriesw1+∞algebracosmologicalconstantcelestialholographynull-coordinategaugespin-coefficientformalismconformallysoftgravitons
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the infinite tower of higher-spin symmetries found in asymptotically flat gravity survives when the vacuum has a cosmological constant. Working in the standard null-coordinate gauge with boundary conditions that allow gravitational flux, the authors derive a hierarchy of evolution equations for charge aspects from the asymptotic Einstein equations, solve them perturbatively to linear order in $\Lambda$, and show that the resulting charges close into the $\Lambda$-deformed $w_{1+\infty}$ algebra, $L_\Lambda w_{1+\infty}$, on a restricted radiative phase space. They also construct curved-space analogues of conformally soft gravitons as spacetime integrals of the radiative data, prove they are $\mathfrak{sl}(2,\mathbb{R})$ primaries, and recover the $\Lambda$-corrected celestial operator product expansion from their Poisson brackets. If correct, this gives a first-principles bulk origin for $L_\Lambda w_{1+\infty}$ and extends the celestial holography dictionary to asymptotically (A)dS$_4$ gravity.

What carries the argument

The load-bearing structure is the hierarchy of evolution equations $$\partial_u Q_s = \eth Q_{s-1} + \tfrac{s+1}{2} C Q_{s-2} - \Lambda \bar{\eth} Q_{s+1},$$ for charge aspects $Q_s$: scalar functionals on the celestial sphere obtained by expanding the Weyl curvature scalars in the null-frame spin-coefficient formalism near the conformal boundary, with $Q_{-2}$ encoding the radiative data and $\eth$ the edth operator acting on the null dyad. For the lowest spins these equations follow from the Bianchi identities and from known asymptotic Einstein equations; the paper assumes their validity for all integer $s\ge -1$. A master charge $\mathcal{Q}_\Lambda[T] = \frac{8}{\kappa^2}\sum_{n=-1}^\infty \int_S T_n Q_n$ is finite and conserved when the dual parameters $T_n$ obey the dual recursion relations, and its Hamiltonian action $\delta^\Lambda_T$ on the boundary data gives a representation of the $\Lambda$-deformed algebroid bracket. Explicit solutions of the dual recursion relations then produce the tower of higher-spin charges, and the same charge action defines the conformally soft graviton operators whose bracket equals the $\Lambda$-deformed OPE.

What would settle it

Derive the next unverified evolution equation, for the spin-4 charge aspect $Q_4$, directly from the Bianchi identities without imposing the single-helicity restriction; if it contains terms not of the form $\Lambda \bar{\eth} Q_5$, the tower of charges and the $L_\Lambda w_{1+\infty}$ algebra fail. Alternatively, compute the Poisson bracket of two quadratic charges to second order in $\Lambda$ and check whether it closes into the same algebra.

Watch

Extended reading notes

Core claim

The central claim is that on the phase space of asymptotically locally (A)dS$_4$ spacetimes with flux-permitting boundary conditions, restricted to the single-helicity sector and truncated to linear order in $\Lambda$ and quadratic order in the fields, an infinite tower of higher-spin charges canonically represents $L_\Lambda w_{1+\infty}$. The charges are built from charge aspects $Q_s$ whose evolution is governed by the hierarchy $\partial_u Q_s = \eth Q_{s-1} + \tfrac{s+1}{2} C Q_{s-2} - \Lambda \bar{\eth} Q_{s+1}$; a master charge $\mathcal{Q}_\Lambda[T]$ is conserved when the dual parameters satisfy dual recursion relations, and its action on the boundary shear provides a representation of the $\Lambda$-deformed bracket. Solving the recursion relations gives explicit linearized and quadratic charges whose Poisson brackets obey the algebra, and the same data define conformally soft graviton operators $G^-_{\Lambda,\Delta}$ that are $\mathfrak{sl}(2,\mathbb{R})$ primaries of the (A)dS$_4$ isometry algebra. Their brackets with the quadratic charges reproduce, from Einstein equations alone, the $\Lambda$-deformed celestial OPE previously proposed on symmetry grounds. The paper therefore claims to supply the missing bulk gravitational derivation of the $L_\Lambda w_{1+\infty}$ symmetry and its OPE.

Load-bearing premise

The chain of charges exists only if the evolution equation verified for the lowest spins continues to hold for every higher spin; the paper assumes this infinite extrapolation and checks only the next case, in a restricted sector.

Editorial extensions

If this is right

  • The celestial bulk-boundary dictionary gains a curved-background entry: the same phase-space Poisson structure that yields $w_{1+\infty}$ in flat space yields $L_\Lambda w_{1+\infty}$ when $\Lambda\neq 0$.
  • The $\Lambda$-deformed conformally soft graviton OPE becomes a derived result rather than an ansatz, so celestial amplitudes in (A)dS$_4$ can use it as an input with a known bulk origin.
  • Asymptotically (A)dS$_4$ spacetimes with radiation acquire an infinite family of renormalized higher-spin charges, extending the low-spin boundary charge algebra to infinite spin.
  • The construction fixes the $\Lambda$-corrections to the transformation of the boundary shear under higher-spin symmetries, giving concrete predictions for how soft limits are deformed by the cosmological constant.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The truncation to linear order in $\Lambda$ and to the single-helicity sector leaves open whether the algebra survives at $\Lambda^2$; if it does not, $L_\Lambda w_{1+\infty}$ is best read as an emergent symmetry of the perturbatively restricted phase space rather than an exact one.
  • A natural next test is to complete the opposite-helicity sector; that completion would either confirm the chiral algebra or produce additional mixed-helicity deformations not visible in the present truncation.
  • If the hierarchy is exact for all spins, the same charges should imply $\Lambda$-corrected soft-graviton theorems; computing the conformally soft limit of a tree-level (A)dS$_4$ graviton amplitude and matching equation (42) would test this directly.
  • The apparent tension between this bulk construction and the light-ray-operator picture in the boundary CFT suggests a precise dictionary question: whether the two sets of higher-spin operators are the same objects seen from spacelike and null defects, or genuinely different sectors.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript studies asymptotically locally (anti-)de Sitter spacetimes in Bondi gauge with boundary conditions that allow gravitational flux. Using Newman-Penrose scalars, it defines charge aspects Q_s by Q_s = Ψ_{2−s}^{(0)} and writes the asymptotic Einstein equations as the recursion relations (14), which it extends to all integer spins s ≥ −1. It introduces a master charge (16) and dual recursion relations (17), and claims that the resulting Noether charges act on the shear through a Λ-deformed transformation (22) that provides a representation of the Λ-deformed symmetry algebroid bracket (26). The paper then constructs linear and quadratic higher-spin charges to first order in Λ and states that they obey the L_Λ w_{1+∞} algebra (48). Finally, it defines Λ-deformed conformally soft gravitons (35), shows they are sl(2,R) primaries, and claims that their Poisson brackets with the charges reproduce the Taylor–Zhu Λ-corrected celestial OPE (55). All detailed computations are deferred to a companion paper [54], which is listed as in preparation.

Significance. If the claims are correct, the paper would establish a bulk gravitational origin for the L_Λ w_{1+∞} algebra and extend the higher-spin symmetry structure of asymptotically flat spacetimes to asymptotically (A)dS_4, thereby adding a new entry to the celestial bulk-boundary dictionary. The construction is well organized and transparent about its main restrictions: single-helicity data, linear order in Λ, and quadratic order in the fields. The explicit charge formulas (31)–(32), (53)–(54), the master-charge regularization, and the proposed identification with Taylor–Zhu operators are concrete and falsifiable, and the authors are candid about the low-spin verification of the recursion relations. The significance is, however, conditional on the validity of the extrapolation of (14) to all higher spins and on the availability of the deferred derivations; without independent verification of those steps, the central claims remain plausible but not established.

major comments (3)
  1. [Recursive equations for charge evolution, Eq. (14)] Equation (14) is the load-bearing input for the entire tower of charges: it is used in the dual recursion (17), the master charge (16)–(18), and the explicit charges (31)–(32) and (53)–(54). The paper establishes (14) from the asymptotic Einstein equations only for s ≤ 2; for s = 3 it states that verification holds only modulo the single-helicity restriction C̄ = 0; and for s > 3 it says it 'expects' (14) to capture subleading Bianchi identities for Ψ_0. Since Q_s is originally defined only for −2 ≤ s ≤ 2, the equations for s ≥ 4 are an extrapolation. If (14) fails at any s ≥ 4, the charges are not derived from the Einstein equations and the representation claim is severed. Please provide a proof or derivation of (14) for all spins used in the construction, or at minimum a verification for all s that appear in the algebra, or make the companion derivation available to referees.
  2. [Higher-spin charges and the L_Λ w_{1+∞} algebra, Eqs. (27), (42), (48)] The three principal results — the representation of the deformed bracket (27), the L_Λ w_{1+∞} algebra of the constructed charges (48), and the match with the Taylor–Zhu OPE (42) — are all stated with the remark that the complete derivation appears in the companion paper [54], which is listed as 'manuscript in preparation' and was not available for review. The refereed text contains only outlines of these computations. As a consequence, the central claims cannot be independently checked from the manuscript alone. I would ask that the detailed calculations behind (27), (48), and (42) be included in an appendix, or that the companion paper be supplied with the submission so that the derivation can be assessed.
  3. [Λ-deformed symmetry algebroid and Eq. (33)] The deformed bracket (26) and the deformed phase-space variable Q_{−2}^Λ in (33) are introduced as 'motivated by' the known L_Λ w_{1+∞} algebra and the Taylor–Zhu OPE. This raises a potential circularity: if these objects are chosen with the target algebra and OPE in mind, then the later agreement is partly by construction. The paper should clarify which ingredients are derived from the Einstein equations and which are imposed as targets. In particular, is Q_{−2}^Λ uniquely fixed by the solution of (14) and (17), or is it selected to reproduce (36)–(42)? If a choice is involved, the bulk-derivation claim should be stated more modestly. A short discussion of the uniqueness or derivation of (33) from the recursion relations would resolve this concern.
minor comments (6)
  1. [Abstract and introduction] The abstract and introduction state the representation result without the qualifications that are explicit later in the letter; it would be helpful to state in the abstract that the result holds to linear order in Λ, to quadratic order in the fields, and in the single-helicity sector.
  2. [After Eq. (22)] The sentence 'This formula generalizes the transformation of the shear obtained in [34] to include the effect of curvature to leading order in Λ' should also state that it is restricted to the single-helicity phase space and to the perturbative order used in the paper.
  3. [Equation (27)] The symbol 'ˆ=' used in Eq. (27) is not defined; please define it explicitly, for example as equality on the support of the dual evolution equations (17).
  4. [Higher-spin charges section] The sentence 'Working to linear order in Λ and C we construct a tower of higher-spin charges' is imprecise because the charges are quadratic in C; please rephrase as 'to first order in Λ and to quadratic order in the fields'.
  5. [Appendix: The L_Λ w_{1+∞} algebra] The discussion of the rescaling freedom (45)–(46) and the phase convention (47) is brief; a few sentences explaining why the phase is necessary for the charge-aspect identification (44) would make the match with (48) easier to follow.
  6. [Equations (38) and (42)] The notation switches between G_{Λ,Δ_2}^{-} and G_{Λ,1−s}^{-} in the derivation of (42); aligning these symbols would improve readability.

Circularity Check

0 steps flagged · score 2.0 of 10

No by-construction circularity; main caveats are an acknowledged spin extrapolation and detailed proofs deferred to a same-author companion paper.

full rationale

Walking the derivation chain, I find no step where a charge, OPE coefficient, or bracket is produced by fitting to the quantity it is then said to predict. The charge aspects Q_s are defined from the Weyl expansion and their u-evolution is taken from the asymptotic Einstein equations; for s=0,1 this reproduces the Lambda-BMS result of [40], and for s=3 the paper states a verification modulo the restriction C-bar=0. The Lambda-deformed bracket (26) is introduced with the known L_Lambda w_{1+infty} algebra (43) as a target, and the phase-space variable Q^Lambda_{-2} in (33) is chosen so that the soft operators are sl(2,R) primaries, which gives the construction a reverse-engineering flavor. However, equations (31)-(32) are obtained by solving the dual recursion (17), not by imposing the target algebra, and the representation identity (27) is an on-shell statement whose main cancellation is outlined in (28)-(29). The real load-bearing weakness is not circularity: the recursion (14) is explicitly 'expected' rather than derived for s>2, and the detailed proofs of (27) and of the TZ-OPE match (42) are deferred to the same-authors companion paper [54]. These are unverified extrapolations and omitted proofs, not a by-construction equivalence between input and output. I therefore find no significant circularity, while noting that the central tower of charges is contingent on the spin extrapolation and on the promised companion computations.

Assumptions & free parameters 0 free parameters · 7 assumptions · 2 invented entities

No numerical parameters are fitted to data. The cosmological constant enters as a physical input, the phase in (47) is a matching convention, and the perturbative truncation is a stated approximation. The deformation operator in (33) is derived from the recursion solutions, not fitted. The higher-spin charges and deformed operators are new conserved quantities and operators, but they are derived from the Einstein equations rather than postulated to explain a result, and they have no independent observable handle yet.

assumptions (7)
  • domain assumption Einstein equations in Bondi-Sachs coordinates with the asymptotic expansion (3) and fall-offs (4).
    The whole construction relies on this gauge and expansion near the conformal boundary, taken from [40,41] and [39].
  • domain assumption Boundary conditions allowing flux through a finite interval of the conformal boundary, with q_AB partial_u q^AB = 0 (eq. (5)).
    These relaxed conditions define the flux-through-boundary phase space and are the starting point for the Lambda-BMS and higher-spin charges.
  • domain assumption Single-helicity restriction: C_bar = 0 (eq. (8)), phase space reduced to {partial_u^-1 C, Q_-2}.
    All algebra statements hold on this restricted phase space only; the other helicity is discarded.
  • domain assumption Truncation to linear order in Lambda and to quadratic order in the fields, neglecting O(Lambda^2) and higher-field terms.
    Charges and algebra are constructed only to this perturbative order, as stated in the introduction and discussion.
  • ad hoc to paper The evolution equations (14) are extended to all integers s >= -1; for s > 2 this is an assumed continuation of the flat-space hierarchy.
    No derivation is shown for s > 2; the paper only notes s=3 works modulo C_bar=0. This is the load-bearing extrapolation.
  • domain assumption Symplectic form (19) and identification of the master charge Q_Lambda[T] as a Noether charge (20)-(21) are correct.
    The paper adopts these from prior work [33,34,38-41,62] without re-deriving them.
  • domain assumption The L_Lambda w1+infinity algebra (43) from [44,45] and the identification of bulk charge aspects Q_s with generators w_s up to a phase (47) are the correct dictionary.
    The matching convention includes a phase i^(1-s) and a Lambda sign redefinition (45)-(46), chosen to make the charge algebra match the known celestial algebra.
invented entities (2)
  • Lambda-deformed higher-spin charge aspects Q_Lambda_s and charges Q_Lambda_s,lin, Q_Lambda_s,quad
    purpose: Generate the Lambda-deformed w1+infinity algebra acting on the gravitational phase space
    They are constructed within the paper as solutions to the recursion relations; no independent observable signature is provided beyond the algebra itself, which is internal to the derivation.
  • Lambda-deformed conformally soft gravitons G_-_Lambda,Delta
    purpose: Bulk spacetime counterparts of the celestial operators in the Taylor-Zhu OPE, defined via the deformed phase space variable Q_Lambda_-2
    These are new composite operators defined in the paper; their only evidence is the internal consistency of the OPE match.

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Pith. "Pith review of Higher-spin charges and the $L_{\Lambda} w_{1 + \infty}$ algebra in (A)dS$_4$." pith.science (2026). https://pith.science/paper/METWGN7F

@misc{pith2026260822625,
  author       = {Pith},
  title        = {Pith review of: Higher-spin charges and the $L_\Lambda w_1 + \infty$ algebra in (A)dS$_4$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/METWGN7F}},
  note         = {Machine review of arXiv:2608.22625}
}
abstract

We consider $(3+1)$-dimensional asymptotically locally (anti-)de Sitter ((A)dS$_4$) spacetimes with boundary conditions allowing for gravitational flux. We construct an infinite tower of higher-spin charges as perturbative solutions in the cosmological constant $\Lambda$ to a hierarchy of evolution equations resulting from an asymptotic expansion of the Einstein equations. We show that these charges canonically realize the $\Lambda$-deformed $w_{1+\infty}$ algebra ($L_{\Lambda} w_{1+\infty}$) on a restricted gravitational phase space, thereby extending the higher-spin symmetry structure of asymptotically flat spacetimes to asymptotically (A)dS spacetimes. We further construct the curved-space counterparts of conformally soft gravitons directly in terms of spacetime data. We show that they are primaries with respect to an $\mathfrak{sl}(2,\mathbb{R})$ subalgebra of the (A)dS$_4$ isometry algebra and that their Poisson brackets with the quadratic higher-spin charges reproduce the $\Lambda$-deformed celestial operator product expansion proposed by Taylor and Zhu. Our results establish the bulk gravitational origin of the $L_{\Lambda}w_{1+\infty}$ symmetry and extend the celestial bulk-boundary dictionary to asymptotically (A)dS$_4$ gravity.

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Works this paper leans on

76 extracted references · 39 canonical work pages

  1. [54]

    Pate, A.-M

    M. Pate, A.-M. Raclariu, A. Strominger, and E. Y. Yuan, Celestial operator products of gluons and gravitons, Rev. Math. Phys.33, 2140003 (2021), arXiv:1910.07424 [hep-th]

    arXiv 2021

  2. [1]

    E. P. Wigner, On Unitary Representations of the Inhomogeneous Lorentz Group, Annals Math.40, 149 (1939)

    work page 1939

  3. [2]

    celestial

    The symplectic structure of asymptotically locally (A)dS4 spacetimes was discussed in [38–41, 62]. In the helicity scalar formalism and subject to the phase space restrictions introduced before, the symplectic form is given by Ω =− 4 κ2 Z I δQ−2∧δ(∂−1 u C).(19) Therefore, the master charge (16) can be expressed as a Noether charge QΛ[T] = lim u→−∞ QΛ[T](u...

    work page

  4. [3]

    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys. B241, 333 (1984)

    work page 1984

  5. [4]

    Weinberg, Dynamical approach to current algebra, Phys

    S. Weinberg, Dynamical approach to current algebra, Phys. Rev. Lett.18, 188 (1967)

    work page 1967

  6. [5]

    Gaiotto, A

    D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized global symmetries, Journal of High Energy Physics2015, 172 (2015)

    2015

  7. [6]

    Coleman,Aspects of Symmetry: Selected Erice Lectures(Cambridge University Press, Cambridge, U.K., 1985)

    S. Coleman,Aspects of Symmetry: Selected Erice Lectures(Cambridge University Press, Cambridge, U.K., 1985)

    work page 1985

  8. [7]

    L. J. Mason and N. M. J. Woodhouse,Integrability, selfduality, and twistor theory(1991)

    work page 1991

Show all 76 references
  1. [8]

    A. B. Zamolodchikov and A. B. Zamolodchikov, Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models, Annals Phys.120, 253 (1979)

    1979

  2. [9]

    Harlow and H

    D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, Communications in Mathematical Physics383, 1669 (2021)

    2021

  3. [10]

    Banks and N

    T. Banks and N. Seiberg, Symmetries and strings in field theory and gravity, Phys. Rev. D83, 084019 (2011)

    2011

  4. [11]

    Bondi, M

    H. Bondi, M. van der Burg, and A. Metzner, Gravitational waves in general relativity. 7. waves from axisymmetric isolated systems, Proc.Roy.Soc.Lond.A269, 21 (1962)

    1962

  5. [12]

    Bondi, Gravitational Waves in General Relativity, Nature186, 535 (1960)

    H. Bondi, Gravitational Waves in General Relativity, Nature186, 535 (1960)

    1960

  6. [13]

    Penrose, Asymptotic properties of fields and space-times, Phys

    R. Penrose, Asymptotic properties of fields and space-times, Phys. Rev. Lett.10, 66 (1963)

    1963

  7. [14]

    R. K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A270, 103 (1962)

    1962

  8. [15]

    Henneaux and C

    M. Henneaux and C. Teitelboim, Asymptotically anti-De Sitter Spaces, Commun. Math. Phys.98, 391 (1985)

    1985

  9. [16]

    J. D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys.104, 207 (1986)

    1986

  10. [17]

    Ashtekar and M

    A. Ashtekar and M. Streubel, Symplectic Geometry of Radiative Modes and Conserved Quantities at Null Infinity, Proc. Roy. Soc. Lond. A376, 585 (1981)

    1981

  11. [18]

    Barnich and C

    G. Barnich and C. Troessaert, Symmetries of asymptotically flat four-dimensional spacetimes at null infinity revisited, Phys. Rev. Lett.105, 111103 (2010)

    2010

  12. [19]

    R. M. Wald and A. Zoupas, A General definition of ’conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D61, 084027 (2000), arXiv:gr-qc/9911095

    2000 arXiv

  13. [20]

    Iyer and R

    V. Iyer and R. M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D50, 846 (1994), arXiv:gr-qc/9403028 [gr-qc]

    1994 arXiv

  14. [21]

    Susskind, The World as a hologram, J

    L. Susskind, The World as a hologram, J. Math. Phys.36, 6377 (1995), arXiv:hep-th/9409089

    1995 arXiv

  15. [22]

    Barnich and F

    G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B633, 3 (2002), arXiv:hep-th/0111246 [hep-th]

    2002 arXiv

  16. [23]

    Aharony, S

    O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323, 183 (2000), arXiv:hep-th/9905111

    2000 arXiv

  17. [24]

    J. M. Maldacena, The LargeNlimit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2, 231 (1998), arXiv:hep-th/9711200

    1998 arXiv

  18. [25]

    T. He, V. Lysov, P. Mitra, and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP05, 151, arXiv:1401.7026 [hep-th]

    arXiv

  19. [26]

    Strominger, On BMS Invariance of Gravitational Scattering, JHEP07, 152, arXiv:1312.2229 [hep-th]

    A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP07, 152, arXiv:1312.2229 [hep-th]

    arXiv

  20. [27]

    Kapec, P

    D. Kapec, P. Mitra, A.-M. Raclariu, and A. Strominger, 2D Stress Tensor for 4D Gravity, Phys. Rev. Lett.119, 121601 (2017), arXiv:1609.00282 [hep-th]

    2017 arXiv

  21. [28]

    Kapec, V

    D. Kapec, V. Lysov, S. Pasterski, and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravityS-matrix, JHEP08, 058, arXiv:1406.3312 [hep-th]

    arXiv

  22. [29]

    Strominger, w 1+∞ algebra and the celestial sphere: Infinite towers of soft graviton, photon, and gluon symmetries, Phys

    A. Strominger, w 1+∞ algebra and the celestial sphere: Infinite towers of soft graviton, photon, and gluon symmetries, Phys. Rev. Lett.127, 221601 (2021)

    2021

  23. [30]

    Guevara, E

    A. Guevara, E. Himwich, M. Pate, and A. Strominger, Holographic symmetry algebras for gauge theory and gravity, Journal of High Energy Physics2021, 152 (2021)

    2021

  24. [31]

    Freidel, D

    L. Freidel, D. Pranzetti, and A.-M. Raclariu, Higher spin dynamics in gravity andw 1+∞ celestial symmetries, Phys. Rev. D106, 086013 (2022)

    2022

  25. [32]

    Freidel, D

    L. Freidel, D. Pranzetti, and A.-M. Raclariu, Sub-subleading soft graviton theorem from asymptotic Einstein’s equations, JHEP05, 186, arXiv:2111.15607 [hep-th]. 9

    arXiv

  26. [33]

    Cresto and L

    N. Cresto and L. Freidel, Asymptotic higher spin symmetries I: covariant wedge algebra in gravity, Letters in Mathematical Physics115, 39 (2025)

    2025

  27. [34]

    Geiller, Celestialw 1+∞ charges and the subleading structure of asymptotically-flat spacetimes, SciPost Phys.18, 023 (2025), arXiv:2403.05195 [hep-th]

    M. Geiller, Celestialw 1+∞ charges and the subleading structure of asymptotically-flat spacetimes, SciPost Phys.18, 023 (2025), arXiv:2403.05195 [hep-th]

    2025 arXiv

  28. [35]

    Adamo, L

    T. Adamo, L. Mason, and A. Sharma, Celestialw 1+∞ Symmetries from Twistor Space, SIGMA18, 016 (2022), arXiv:2110.06066 [hep-th]

    2022 arXiv

  29. [36]

    Cresto and L

    N. Cresto and L. Freidel, Asymptotic higher spin symmetries II: Noether realization in gravity, Journal of High Energy Physics2026, 147 (2026)

    2026

  30. [37]

    A. Kmec, L. Mason, and R. Ruzziconi, Quasi-Local Celestial Charges and Multipoles, (2026), arXiv:2604.13362 [hep-th]

    2026 arXiv

  31. [38]

    A. Kmec, L. Mason, R. Ruzziconi, and A. Yelleshpur Srikant, CelestialLw 1+∞ charges from a twistor action, JHEP10, 250, arXiv:2407.04028 [hep-th]

    arXiv

  32. [39]

    Poole, K

    A. Poole, K. Skenderis, and M. Taylor, (A)dS 4 in Bondi gauge, Class. Quant. Grav.36, 095005 (2019), arXiv:1812.05369 [hep-th]

    2019 arXiv

  33. [40]

    Compere and D

    G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav.25, 195014 (2008), arXiv:0805.1902 [hep-th]

    2008 arXiv

  34. [41]

    Comp` ere, A

    G. Comp` ere, A. Fiorucci, and R. Ruzziconi, The Λ-BMS4 charge algebra, Journal of High Energy Physics2020, 205 (2020)

    2020

  35. [42]

    38, 229501 (2021)]

    Comp` ere, Geoffrey and Fiorucci, Adrien and Ruzziconi, Romain, The Λ-BMS4 group of dS4 and new boundary conditions for AdS4, Classical and Quantum Gravity36, 195017 (2019), [Erratum: Class.Quant.Grav. 38, 229501 (2021)]

    2019

  36. [43]

    D. B. Fairlie and J. Nuyts, Deformations and Renormalizations of W(infinity), Commun. Math. Phys.134, 413 (1990)

    1990

  37. [44]

    From a twistor perspective, it was shown in [45] that a non-vanishing cosmological constant yields the same deformation of thew 1+∞ algebra

    to arise from a rather simple,sl(2,R) covariant mod- ification of the OPE of conformally soft gravitons in 4d flat spacetime. From a twistor perspective, it was shown in [45] that a non-vanishing cosmological constant yields the same deformation of thew 1+∞ algebra. More re- c...

    2026 arXiv

  38. [45]

    C. N. Pope, L. J. Romans, and X. Shen, The Complete Structure of W(Infinity), Phys. Lett. B236, 173 (1990)

    1990

  39. [46]

    T. R. Taylor and B. Zhu, w1+∞ algebra with a cosmological constant and the celestial sphere, Phys. Rev. Lett.132, 221602 (2024)

    2024

  40. [47]

    Bittleston, G

    R. Bittleston, G. Bogna, S. Heuveline, A. Kmec, L. Mason, and D. Skinner, On AdS 4 deformations of celestial symmetries, JHEP07, 010, arXiv:2403.18011 [hep-th]

    arXiv

  41. [48]

    Strominger and H

    A. Strominger and H. Wei, EVERY CFT 3 HAS ANL Λw1+∞ SYMMETRY (2026), arXiv:2603.26459 [hep-th]

    2026

  42. [49]

    Newman and R

    E. Newman and R. Penrose, An Approach to gravitational radiation by a method of spin coefficients, J. Math. Phys.3, 566 (1962)

    1962

  43. [50]

    E. T. Newman and R. Penrose, New conservation laws for zero rest-mass fields in asymptotically flat space-time, Proc. Roy. Soc. Lond. A305, 175 (1968)

    1968

  44. [51]

    Barnich, P

    G. Barnich, P. Mao, and R. Ruzziconi, BMS current algebra in the context of the Newman–Penrose formalism, Class. Quant. Grav.37, 095010 (2020), arXiv:1910.14588 [gr-qc]

    2020 arXiv

  45. [52]

    Freidel and D

    L. Freidel and D. Pranzetti, Gravity from symmetry: duality and impulsive waves, JHEP04, 125, arXiv:2109.06342 [hep-th]

    arXiv

  46. [53]

    Guevara, Notes on Conformal Soft Theorems and Recursion Relations in Gravity, (2019), arXiv:1906.07810 [hep-th]

    A. Guevara, Notes on Conformal Soft Theorems and Recursion Relations in Gravity, (2019), arXiv:1906.07810 [hep-th]

    2019 arXiv

  47. [55]

    Puhm, Conformally Soft Theorem in Gravity, JHEP09, 130, arXiv:1905.09799 [hep-th]

    A. Puhm, Conformally Soft Theorem in Gravity, JHEP09, 130, arXiv:1905.09799 [hep-th]

    1905 arXiv

  48. [56]

    Di Giacomo, M

    L. Di Giacomo, M. Micol, D. Pranzetti, and A.-M. Raclariu, (2026), manuscript in preparation

    2026

  49. [57]

    de Haro, K

    S. de Haro, K. Skenderis, and S. N. Solodukhin, Holographic reconstruction of spacetime and renormalization in the ads/cft correspondence, Communications in Mathematical Physics217, 595–622 (2001)

    2001

  50. [58]

    For Λ<0 (Λ>0) it is a timelike (spacelike) surface of codimension 1

    Strictly speaking,Iis the portion of conformal boundary reached by the null rays identified by (u, x A). For Λ<0 (Λ>0) it is a timelike (spacelike) surface of codimension 1

  51. [59]

    Then,{q AB, J CD}form a canonically conjugated pair

    The degrees of freedom inE T F AB can be expressed via the auxiliary quantityJ AB, the traceless, angular part of the holographic stress energy tensor. Then,{q AB, J CD}form a canonically conjugated pair. Please refer to [40] for more details

  52. [60]

    Geiller and C

    M. Geiller and C. Zwikel, The partial Bondi gauge: Further enlarging the asymptotic structure of gravity, SciPost Phys. 13, 108 (2022)

    2022

  53. [61]

    In going from spin-jtensors to helicity-sscalars through the contractionO s =O A1...Aj mA1 0 . . . m Aj 0 , withs(m A 0 ) = +1, the first label is traded for the second; negative helicity-sscalars are obtained through the contraction with the complex conjugate dyad ass( ¯mA 0 ) =−1

  54. [62]

    Saw, Mass-loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant, Phys

    V.-L. Saw, Mass-loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant, Phys. Rev. D94, 104004 (2016), arXiv:1605.05151 [gr-qc]

    2016 arXiv

  55. [63]

    Mao, Asymptotics with a cosmological constant: The solution space, Phys

    P. Mao, Asymptotics with a cosmological constant: The solution space, Phys. Rev. D99, 104024 (2019)

    2019

  56. [64]

    Papadimitriou and K

    I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, JHEP08, 004, arXiv:hep- th/0505190

  57. [65]

    L. K. Norris, Schouten-nijenhuis brackets, Journal of Mathematical Physics38, 2694 (1997)

    1997

  58. [66]

    L. F. Alday, T. Hansen, and J. A. Silva, AdS Virasoro-Shapiro from dispersive sum rules, JHEP10, 036, arXiv:2204.07542 [hep-th]

    arXiv

  59. [67]

    L. F. Alday, T. Hansen, and J. A. Silva, AdS Virasoro-Shapiro from single-valued periods, JHEP12, 010, arXiv:2209.06223 [hep-th]. 10

    arXiv

  60. [68]

    L. F. Alday, T. Hansen, and J. A. Silva, Emergent Worldsheet for the AdS Virasoro-Shapiro Amplitude, Phys. Rev. Lett. 131, 161603 (2023), arXiv:2305.03593 [hep-th]

    2023 arXiv

  61. [69]

    L. F. Alday and T. Hansen, The AdS Virasoro-Shapiro amplitude, JHEP10, 023, arXiv:2306.12786 [hep-th]

    arXiv

  62. [70]

    I. M. Gelfand, M. I. Graev, and N. Y. Vilenkin,Generalized functions -Integral geometry and representation theory, Vol. 5 (Academic Press, 1966)

    1966

  63. [71]

    Pasterski, A

    S. Pasterski, A. Puhm, and E. Trevisani, Celestial diamonds: conformal multiplets in celestial CFT, JHEP11, 072, arXiv:2105.03516 [hep-th]

    arXiv

  64. [72]

    Pranzetti and D

    D. Pranzetti and D. G. Salluce, Double-soft limit and celestial shadow OPE from charge bracket, JHEP03, 096, arXiv:2510.26520 [hep-th]

  65. [73]

    I. R. Klebanov and A. M. Polyakov, AdS dual of the critical O(N) vector model, Phys. Lett. B550, 213 (2002), arXiv:hep- th/0210114

    2002

  66. [74]

    Bagger and N

    J. Bagger and N. Lambert, Modeling Multiple M2’s, Phys. Rev. D75, 045020 (2007), arXiv:hep-th/0611108

    2007 arXiv

  67. [75]

    Aharony, O

    O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10, 091, arXiv:0806.1218 [hep-th]

    arXiv

  68. [76]

    Drukker, M

    N. Drukker, M. Marino, and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys.306, 511 (2011), arXiv:1007.3837 [hep-th]

    2011 arXiv

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