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arxiv: 2601.00096 · v2 · submitted 2025-12-31 · ✦ hep-th · gr-qc

Soft Algebras in AdS₄ from Light Ray Operators in CFT₃

Ahmed Sheta , Andrew Strominger , Adam Tropper , Hongji Wei This is my paper

Pith reviewed 2026-05-16 18:00 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords soft algebrasAdS4CFT3light ray operatorsconformal mapasymptotic symmetriesholographysoft gluons
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The pith

A conformal map from flat space to AdS4 sends leading soft gluons to light transforms of conserved currents in the boundary CFT3.

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

The paper shows that the asymptotic S-algebra generated by soft gluons in Minkowski space has a direct counterpart in AdS4. Under a specific conformal map to the Einstein cylinder, the weighted null-line integrals that define the leading soft gluons become light transforms of the global symmetry currents living on the AdS4 boundary. The full tower of generators for the S-algebra is then obtained by acting with the SO(3,2) conformal descendants on these light-transformed operators. This supplies an explicit dictionary between the soft symmetries of flat space and the holographic symmetries realized in the three-dimensional CFT.

Core claim

The leading soft gluons of conformally invariant nonabelian gauge theories on M4, expressed as weighted null line integrals on I+, map under the chosen conformal transformation to light transforms of the conserved global symmetry currents in the boundary CFT3 of AdS4. The complete set of S-algebra generators in the CFT3 is realized by the tower of light-ray operators obtained from the SO(3,2) descendants of this light transform.

What carries the argument

The conformal map that aligns null generators of I+ with antipodally-terminating null geodesic segments on the AdS4 boundary, together with the light transform applied to conserved currents.

If this is right

  • The full tower of S-algebra generators in flat space is realized by SO(3,2) descendants of light transforms in the AdS4 CFT3.
  • Holographic symmetry algebras in M4 and AdS4 are connected through this boundary dictionary.
  • Soft gluon operators on I+ become operators built from conserved currents in the dual CFT3.
  • The construction applies to any conformally invariant nonabelian gauge theory in four dimensions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same geometric alignment may allow flat-space memory effects to be read off from correlation functions in the AdS4 CFT3.
  • The dictionary could extend to include higher-spin or fermionic soft operators by repeating the light-transform construction on the corresponding currents.
  • Testing the algebra at higher orders in the soft expansion would clarify whether the map remains an isomorphism beyond the leading term.

Load-bearing premise

The chosen conformal maps must preserve the action of the soft operators while making the null generators of I+ coincide with the antipodal null geodesics on the AdS4 boundary.

What would settle it

An explicit computation of the commutators among the mapped light-ray operators to check whether they reproduce the S-algebra relations of the boundary CFT3.

read the original abstract

Flat Minkowski space (M$^4$) and AdS$_4$ can both be conformally mapped to the Einstein cylinder. The maps may be judiciously chosen so that some null generators of the $\mathcal{I}^+$ boundary of M$^4$ coincide with antipodally-terminating null geodesic segments on the boundary of AdS$_4$. Conformally invariant nonabelian gauge theories in M$^4$ have an asymptotic $S$-algebra generated by a tower of soft gluons given by weighted null line integrals on $\mathcal{I}^+$. We show that, under the conformal map to AdS$_4$, the leading soft gluons are dual to light transforms of the conserved global symmetry currents in the boundary CFT$_3$. The tower of light ray operators obtained from the $SO(3,2)$ descendants of this light transform realize a full set of generators of the $S$-algebra in the boundary CFT$_3$. This provides a direct connection between holographic symmetry algebras in M$^4$ and AdS$_4$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript shows that, by conformally mapping Minkowski space and AdS4 to the Einstein cylinder with judiciously chosen maps that align certain null generators of I+ with antipodally terminating null geodesics on the AdS boundary, the leading soft gluons of nonabelian gauge theories on I+ are dual to light transforms of conserved global symmetry currents in the boundary CFT3. The SO(3,2) descendants of these light transforms are claimed to generate the full S-algebra in the CFT3, establishing a direct link between flat-space asymptotic symmetries and AdS holographic symmetries.

Significance. If the operator correspondence is rigorously established, the result provides a concrete bridge between soft gluon algebras in flat space and symmetry structures in AdS/CFT, potentially unifying aspects of infrared physics across these settings and offering new tools for studying holographic symmetries via light-ray operators.

major comments (2)
  1. [3] Section 3: The central claim that the conformal map preserves the action of the soft operators (including the weighted null integrals) without extra contact terms or anomalies is stated but not verified explicitly for the nonabelian case; the abstract notes that the maps 'may be judiciously chosen' and 'preserves the action,' yet the load-bearing intertwining property requires a concrete check against the nonlinear S-algebra structure.
  2. [4] Section 4, around the SO(3,2) descendants: The construction of the tower of light-ray operators is outlined, but the explicit verification that these operators satisfy the full commutation relations of the S-algebra (beyond the leading soft gluons) is not provided, leaving the claim that they 'realize a full set of generators' dependent on an unshown closure.
minor comments (2)
  1. [1] The definition of the light transform operator and its relation to the conserved currents could be stated more explicitly in the introduction for clarity.
  2. A few references to prior work on celestial soft algebras and light-ray operators in CFT are present but could be expanded to better situate the novelty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments. We address each major comment below and will revise the manuscript to incorporate explicit verifications where needed.

read point-by-point responses

  1. Referee: Section 3: The central claim that the conformal map preserves the action of the soft operators (including the weighted null integrals) without extra contact terms or anomalies is stated but not verified explicitly for the nonabelian case; the abstract notes that the maps 'may be judiciously chosen' and 'preserves the action,' yet the load-bearing intertwining property requires a concrete check against the nonlinear S-algebra structure.

    Authors: We agree that an explicit check for the nonabelian case strengthens the result. The conformal invariance of the gauge theory and the specific alignment of null generators ensure the map preserves the leading soft gluon action, but we will add a direct computation in revised Section 3 verifying the intertwining for the full nonlinear S-algebra, including explicit confirmation that no extra contact terms arise in the commutators. revision: yes

  2. Referee: Section 4, around the SO(3,2) descendants: The construction of the tower of light-ray operators is outlined, but the explicit verification that these operators satisfy the full commutation relations of the S-algebra (beyond the leading soft gluons) is not provided, leaving the claim that they 'realize a full set of generators' dependent on an unshown closure.

    Authors: We acknowledge the point. The manuscript uses the known representation theory of SO(3,2) and the structure of the S-algebra to argue that the descendants generate the full set, but we agree an explicit closure check is warranted. In the revision we will add this verification (likely as an appendix), computing the commutators of the light-ray operators to confirm they close into the complete S-algebra. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses explicit conformal map and SO(3,2) action without reducing to self-definition or fitted inputs

full rationale

The paper's central step is to select a conformal map from M4 to the Einstein cylinder such that I+ null generators align with AdS4 boundary geodesics, then explicitly map weighted null integrals of soft gluons to light transforms of CFT3 currents and generate the full S-algebra via SO(3,2) descendants. This is presented as a derived correspondence rather than an input assumption or renamed known result. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or ansatz smuggled from prior work; the abstract and construction remain self-contained against the geometric alignment and operator intertwining shown in the text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, new entities, or additional axioms are stated beyond the standard assumption of conformal invariance of the gauge theory.

axioms (1)
  • domain assumption The gauge theories are conformally invariant so that the soft S-algebra is well-defined.
    Required for the existence of the weighted null-line integrals that generate the S-algebra.

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Asymptotic charges as detectors and the memory effect in massive QED and perturbative quantum gravity

    hep-th 2026-04 unverdicted novelty 6.0

    Faddeev-Kulish dressings correctly encode the memory effect in in and out Fock spaces for massive QED and perturbative quantum gravity, with physical contributions to memory eigenvalues from the dressings.

  2. Quasi-Local Celestial Charges and Multipoles

    hep-th 2026-04 unverdicted novelty 6.0

    Explicit quasi-local formulae for celestial higher-spin charges and multipoles are given on finite 2-surfaces using higher-valence twistor solutions, with a phase-space derivation from self-dual gravity.

  3. Note on higher spins and holographic symmetry algebra

    hep-th 2026-02 unverdicted novelty 4.0

    Higher spin particles generate w_∞ and S-algebra subalgebras inside the soft holographic symmetry algebra that do not commute with the graviton and gluon versions.

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages · cited by 3 Pith papers · 15 internal anchors

  1. [1]

    Guevara, E

    A. Guevara, E. Himwich, M. Pate, and A. Strominger,Holographic symmetry algebras for gauge theory and gravity,JHEP11(2021) 152, [arXiv:2103.03961]

    work page arXiv 2021

  2. [2]

    Strominger,w1+∞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(2021), no. 22 221601, [arXiv:2105.14346]

    work page arXiv 2021

  3. [3]

    Penrose,The Nonlinear Graviton,Gen

    R. Penrose,The Nonlinear Graviton,Gen. Rel. Grav.7(1976) 171–176

    work page 1976

  4. [4]

    R. S. Ward,On Selfdual gauge fields,Phys. Lett. A61(1977) 81–82. 20

    work page 1977

  5. [5]

    Costello and N

    K. Costello and N. M. Paquette,Celestial holography meets twisted holography: 4d amplitudes from chiral correlators,JHEP10(2022) 193, [arXiv:2201.02595]

    work page arXiv 2022

  6. [6]

    Costello, N

    K. Costello, N. M. Paquette, and A. Sharma,Top-Down Holography in an Asymptotically Flat Spacetime,Phys. Rev. Lett.130(2023), no. 6 061602, [arXiv:2208.14233]

    work page arXiv 2023

  7. [7]

    Celestial w1+∞ Symmetries from Twistor Space,

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

    work page arXiv 2022

  8. [8]

    A. Kmec, L. Mason, R. Ruzziconi, and A. Sharma,S-algebra in gauge theory: twistor, spacetime and holographic perspectives,Class. Quant. Grav.42(2025), no. 19 195008, [arXiv:2506.01888]

    work page arXiv 2025

  9. [9]

    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(1986) 207–226

    work page 1986

  10. [10]

    J. M. Maldacena,The LargeNlimit of superconformal field theories and supergravity,Adv. Theor. Math. Phys.2(1998) 231–252, [hep-th/9711200]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  11. [11]

    Large N Field Theories, String Theory and Gravity

    O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz,Large N field theories, string theory and gravity,Phys. Rept.323(2000) 183–386, [hep-th/9905111]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  12. [12]

    Dimensional Reduction in Quantum Gravity

    G. ’t Hooft,Dimensional reduction in quantum gravity,Conf. Proc. C930308(1993) 284–296, [gr-qc/9310026]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  13. [13]

    The World as a Hologram

    L. Susskind,The World as a hologram,J. Math. Phys.36(1995) 6377–6396, [hep-th/9409089]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  14. [14]

    L. P. de Gioia and A.-M. Raclariu,Celestial sector in CFT: Conformally soft symmetries, SciPost Phys.17(2024), no. 1 002, [arXiv:2303.10037]

    work page arXiv 2024

  15. [15]

    L. P. de Gioia and A.-M. Raclariu,Celestial amplitudes from conformal correlators with bulk-point kinematics,arXiv:2405.07972

    work page arXiv

  16. [16]

    L. P. de Gioia and A.-M. Raclariu,Infinite towers of 2d symmetry algebras from Carrollian limit of 3d CFT,arXiv:2508.19981

    work page arXiv

  17. [17]

    R. S. Ward,Self-dual space-times with cosmological constant,Communications in Mathematical Physics78(1980), no. 1 1–17

    work page 1980

  18. [18]

    T. R. Taylor and B. Zhu,w1+∞Algebra with a Cosmological Constant and the Celestial Sphere,Phys. Rev. Lett.132(2024), no. 22 221602, [arXiv:2312.00876]. 21

    work page arXiv 2024

  19. [19]

    Bittleston, G

    R. Bittleston, G. Bogna, S. Heuveline, A. Kmec, L. Mason, and D. Skinner,On AdS 4 deformations of celestial symmetries,JHEP07(2024) 010, [arXiv:2403.18011]

    work page arXiv 2024

  20. [20]

    N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals

    O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena,N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,JHEP10(2008) 091, [arXiv:0806.1218]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  21. [21]

    D. M. Hofman and J. Maldacena,Conformal collider physics: Energy and charge correlations,JHEP05(2008) 012, [arXiv:0803.1467]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  22. [22]

    Modular Hamiltonians on the null plane and the Markov property of the vacuum state,

    H. Casini, E. Teste, and G. Torroba,Modular Hamiltonians on the null plane and the Markov property of the vacuum state,J. Phys. A50(2017), no. 36 364001, [arXiv:1703.10656]

    work page arXiv 2017

  23. [23]

    Weight Shifting Operators and Conformal Blocks,

    D. Karateev, P. Kravchuk, and D. Simmons-Duffin,Weight Shifting Operators and Conformal Blocks,JHEP02(2018) 081, [arXiv:1706.07813]

    work page arXiv 2018

  24. [24]

    Light-ray Operators and the BMS Algebra

    C. C´ ordova and S.-H. Shao,Light-ray Operators and the BMS Algebra,Phys. Rev. D98 (2018), no. 12 125015, [arXiv:1810.05706]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  25. [25]

    Light-ray operators in conformal field theory,

    P. Kravchuk and D. Simmons-Duffin,Light-ray operators in conformal field theory,JHEP 11(2018) 102, [arXiv:1805.00098]

    work page arXiv 2018

  26. [26]

    The light-ray OPE and conformal colliders,

    M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov,The light-ray OPE and conformal colliders,JHEP01(2021) 128, [arXiv:1905.01311]

    work page arXiv 2021

  27. [27]

    Kologlu, P

    M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov,Shocks, Superconvergence, and a Stringy Equivalence Principle,JHEP11(2020) 096, [arXiv:1904.05905]

    work page arXiv 2020

  28. [28]

    Belin, D

    A. Belin, D. M. Hofman, G. Mathys, and M. T. Walters,On the stress tensor light-ray operator algebra,JHEP05(2021) 033, [arXiv:2011.13862]

    work page arXiv 2021

  29. [29]

    Huang,Stress-tensor commutators in conformal field theories near the lightcone, Phys

    K.-W. Huang,Stress-tensor commutators in conformal field theories near the lightcone, Phys. Rev. D100(2019), no. 6 061701, [arXiv:1907.00599]

    work page arXiv 2019

  30. [30]

    Huang,Lightcone Commutator and Stress-Tensor Exchange ind >2CFTs,Phys

    K.-W. Huang,Lightcone Commutator and Stress-Tensor Exchange ind >2CFTs,Phys. Rev. D102(2020), no. 2 021701, [arXiv:2002.00110]

    work page arXiv 2020

  31. [31]

    Kabat, G

    D. Kabat, G. Lifschytz, P. Nguyen, and D. Sarkar,Light-ray moments as endpoint contributions to modular Hamiltonians,JHEP09(2021) 074, [arXiv:2103.08636]. 22

    work page arXiv 2021

  32. [32]

    He and P

    T. He and P. Mitra,New magnetic symmetries in(d+ 2)-dimensional QED,JHEP01 (2021) 122, [arXiv:1907.02808]

    work page arXiv 2021

  33. [33]

    Donnay, G

    L. Donnay, G. Giribet, and F. Rosso,Quantum BMS transformations in conformally flat space-times and holography,JHEP12(2020) 102, [arXiv:2008.05483]

    work page arXiv 2020

  34. [34]

    Gonzo and A

    R. Gonzo and A. Pokraka,Light-ray operators, detectors and gravitational event shapes, JHEP05(2021) 015, [arXiv:2012.01406]

    work page arXiv 2021

  35. [35]

    Hu and S

    Y. Hu and S. Pasterski,Celestial conformal colliders,JHEP02(2023) 243, [arXiv:2211.14287]

    work page arXiv 2023

  36. [36]

    Carrollian Perspective on Celestial Holography

    L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi,Carrollian Perspective on Celestial Holography,Phys. Rev. Lett.129(2022), no. 7 071602, [arXiv:2202.04702]

    work page internal anchor Pith review arXiv 2022

  37. [37]

    Donnay, A

    L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi,Bridging Carrollian and celestial holography,Phys. Rev. D107(2023), no. 12 126027, [arXiv:2212.12553]

    work page arXiv 2023

  38. [38]

    Hu and S

    Y. Hu and S. Pasterski,Detector operators for celestial symmetries,JHEP12(2023) 035, [arXiv:2307.16801]

    work page arXiv 2023

  39. [39]

    H. A. Gonz´ alez and J. Salzer,Energy Detectors and Asymptotic Symmetries, arXiv:2510.27348

    work page arXiv

  40. [40]

    Moult, S

    I. Moult, S. A. Narayanan, and S. Pasterski,Memory Correlators and Ward Identities in the ’in-in’ Formalism,arXiv:2512.02825

    work page arXiv

  41. [41]

    Light-ray Operators and the w 1+∞ Algebra,

    E. Himwich and M. Pate,Light-ray Operators and thew 1+∞ Algebra,arXiv:2512.18973

    work page arXiv

  42. [42]

    The self-dual sector of QCD amplitudes

    G. Chalmers and W. Siegel,The Selfdual sector of QCD amplitudes,Phys. Rev. D54 (1996) 7628–7633, [hep-th/9606061]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  43. [43]

    A. Ball, S. A. Narayanan, J. Salzer, and A. Strominger,Perturbatively exact w 1+∞ asymptotic symmetry of quantum self-dual gravity,JHEP01(2022) 114, [arXiv:2111.10392]

    work page arXiv 2022

  44. [44]

    Costello and D

    K. Costello and D. Gaiotto,Twisted holography,JHEP01(2025) 087, [arXiv:1812.09257]

    work page arXiv 2025

  45. [45]

    K. J. Costello,Bootstrapping two-loop QCD amplitudes,JHEP08(2025) 011, [arXiv:2302.00770]. 23

    work page arXiv 2025

  46. [46]

    Self-Dual Gauge Theory from the Top Down

    R. Bittleston, K. Costello, and K. Zeng,Self-Dual Gauge Theory from the Top Down, arXiv:2412.02680

    work page internal anchor Pith review Pith/arXiv arXiv

  47. [47]

    Banks and A

    T. Banks and A. Zaks,On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions,Nucl. Phys. B196(1982) 189–204

    work page 1982

  48. [48]

    Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories

    N. Seiberg,Electric - magnetic duality in supersymmetric nonAbelian gauge theories,Nucl. Phys. B435(1995) 129–146, [hep-th/9411149]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  49. [49]

    Asymptotic Symmetries of Yang-Mills Theory

    A. Strominger,Asymptotic Symmetries of Yang-Mills Theory,JHEP07(2014) 151, [arXiv:1308.0589]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  50. [50]

    T. He, P. Mitra, and A. Strominger,2D Kac-Moody Symmetry of 4D Yang-Mills Theory, JHEP10(2016) 137, [arXiv:1503.02663]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  51. [51]

    Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory

    A. Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory. Princeton University Press, 2018

    work page 2018

  52. [52]

    A. J. Larkoski,Conformal Invariance of the Subleading Soft Theorem in Gauge Theory, Phys. Rev. D90(2014), no. 8 087701, [arXiv:1405.2346]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  53. [53]

    H. Z. Chen, R. C. Myers, and A.-M. Raclariu,Entanglement, soft modes, and celestial holography,Phys. Rev. D109(2024), no. 12 L121702, [arXiv:2308.12341]

    work page arXiv 2024

  54. [54]

    Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere

    S. Pasterski, S.-H. Shao, and A. Strominger,Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere,Phys. Rev. D96(2017), no. 6 065026, [arXiv:1701.00049]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  55. [55]

    Pasterski and S.-H

    S. Pasterski and S.-H. Shao,Conformal basis for flat space amplitudes,Physical Review D 96(Sept., 2017)

    work page 2017

  56. [56]

    S. Jain, D. K. S, and E. Skvortsov,Hidden sectors of Chern-Simons matter theories and exact holography,Phys. Rev. D111(2025), no. 10 106017, [arXiv:2405.00773]

    work page arXiv 2025

  57. [57]

    Aharony, R

    O. Aharony, R. R. Kalloor, and T. Kukolj,A chiral limit for Chern-Simons-matter theories,JHEP10(2024) 051, [arXiv:2405.01647]

    work page arXiv 2024

  58. [58]

    Melton and A

    W. Melton and A. Strominger,Conformal Field Theory with Periodic Time, arXiv:2512.09089. 24

    work page arXiv