pith. sign in

arxiv: 2605.16641 · v1 · pith:YMDOUNAWnew · submitted 2026-05-15 · ✦ hep-th

On bulk reconstruction in Lorentzian AdS and its flat space limit

N\'uria Navarro , Ana-Maria Raclariu This is my paper

Pith reviewed 2026-05-20 15:46 UTC · model grok-4.3

classification ✦ hep-th
keywords bulk reconstructionLorentzian AdSfree scalar fieldtime-ordered propagatorsflat space limitCFT primariesshadow operatorscanonical quantization
0
0 comments X

The pith

Free scalar fields on a codimension-1 hypersurface in Lorentzian AdS4 can be reconstructed from boundary CFT operators integrated with time-ordered or anti-time-ordered propagators over past or future regions.

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

The paper shows how to express a free scalar field living on a bulk slice in AdS4 directly in terms of boundary primary operators. Positive-energy and negative-energy solutions to the Klein-Gordon equation are built from bulk-to-boundary propagators that carry definite time orderings. This produces a reconstruction formula in which the bulk field is an integral of CFT operators over boundary regions lying entirely to the past or future of the slice, with kernels given by the corresponding propagators. The same construction recovers the canonical quantization of a free scalar in flat space when the AdS radius is sent to infinity, either in a plane-wave basis or in a Carrollian basis depending on how the conformal dimension is scaled. Equivalent expressions are obtained by using shadow operators instead of primaries.

Core claim

Free scalar fields on a codimension-1 bulk hypersurface Σ_τ can be expressed in terms of operators integrated over boundary regions in the past or future of Σ_τ with kernels given by time-ordered or anti-time-ordered propagators. The positive and negative energy subspaces of Klein-Gordon solutions in AdS are spanned by bulk-to-boundary propagators carrying the appropriate time orderings. The resulting map is shown both representation-theoretically and by explicit flat-space limits to be the direct AdS analog of canonical quantization of a free scalar.

What carries the argument

Time-ordered and anti-time-ordered bulk-to-boundary propagators that span the positive- and negative-energy subspaces of Klein-Gordon solutions.

If this is right

  • The bulk field admits equivalent representations using either CFT primaries or their shadow operators.
  • Taking the conformal dimension to infinity yields a plane-wave decomposition of the scalar.
  • Keeping the conformal dimension fixed produces a Carrollian decomposition.
  • The scalar can alternatively be expanded in wavefunctions belonging to principal-series representations of an so(3,1) subalgebra, which become ordinary conformal primary wavefunctions in flat space.

Where Pith is reading between the lines

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

  • The same time-ordering technique could be used to reconstruct higher-spin fields by replacing the scalar propagator with the appropriate spin-s propagator.
  • The flat-space limit construction supplies a concrete dictionary between AdS boundary operators and Carrollian or celestial operators that might be useful for flat-space holography.
  • One could test the reconstruction by verifying that the reconstructed field satisfies the correct bulk two-point function when the two points lie on the hypersurface.

Load-bearing premise

The positive and negative energy subspaces of Klein-Gordon solutions in AdS4 are spanned by bulk-to-boundary propagators carrying appropriate time orderings.

What would settle it

An explicit check that the commutator of two reconstructed fields on Σ_τ fails to reproduce the standard bulk commutator function derived from the Klein-Gordon equation.

Figures

Figures reproduced from arXiv: 2605.16641 by Ana-Maria Raclariu, N\'uria Navarro.

Figure 1
Figure 1. Figure 1: Left: The HKLL formula allows for the bulk field in the colored regions to be reconstructed [PITH_FULL_IMAGE:figures/full_fig_p018_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The normalizable component of a bulk field on Σ [PITH_FULL_IMAGE:figures/full_fig_p028_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Foliations of Lorentzian AdS4. 6.1 Hyperbolic foliation The orbits of the Lorentz SO(3, 1) subgroup of SO(3, 2) that fixes the origin are hyperbolic AdS3, dS3 slices and the null cone through the origin. One way to identify the decomposition of so(3, 2) into representations of so(3, 1) is to solve the wave equation in a foliation of AdS4 with (A)dS3 and null slices. Reorganizing the solution to the wave eq… view at source ↗
Figure 4
Figure 4. Figure 4: AdS-bulk-to-boundary propagators become proportional to massless plane waves in the flat [PITH_FULL_IMAGE:figures/full_fig_p048_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Taking B to be an infinitesimal strip around a constant time slice of the boundary allows for the field to be reconstructed in the central diamond. For fixed ∆, our proposed AdS4 reconstruction formulas reduce to the expansion of a free field in flat space in a basis of Carrollian wavefunctions. The modes in this expansion identify, upon quantization, operators in a 3d Carrollian field theory with shadow t… view at source ↗
Figure 6
Figure 6. Figure 6: Location of poles in the integrand of (C.9). [PITH_FULL_IMAGE:figures/full_fig_p063_6.png] view at source ↗
read the original abstract

We revisit the reconstruction of a free quantum field in 4-dimensional Lorentzian Anti-de-Sitter (AdS$_4$) spacetime in terms of primary operators in the boundary 3d CFT (CFT$_3$). We show that the positive and negative energy subspaces of solutions to the Klein-Gordon equation in AdS can be spanned with bulk-to-boundary propagators with appropriate time orderings. As a result, free scalar fields on a codimension-1 bulk hypersurface $\Sigma_{\tau}$ can be expressed in terms of operators integrated over boundary regions in the past or future of $\Sigma_{\tau}$ with kernels given by time-ordered or anti-time-ordered propagators. We present various equivalent representations for the bulk field in terms of either CFT primaries or their shadows. We show from both a representation theoretic perspective and by direct computation of various flat space limits that our construction is the AdS analog of the canonical quantization of a free scalar in flat space. Depending on the choice of $\Delta$ and the location of the boundary insertions one obtains a decomposition of the scalar in either a plane wave basis ($\Delta \rightarrow \infty$) or a Carrollian basis (fixed $\Delta$). Finally, we show that the free scalar in AdS$_4$ can be alternatively decomposed in terms of wavefunctions associated with principal series representations of dimension $\delta = 1 + i\lambda$ of an $\mathfrak{so}(3,1)$ subalgebra of the AdS$_4$ isometry algebra. We demonstrate that the latter become, in the limit of large AdS radius and for fixed $\delta$, scalar conformal primary wavefunctions in flat space.

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

1 major / 2 minor

Summary. The manuscript claims that free scalar fields on a codimension-1 bulk hypersurface Σ_τ in Lorentzian AdS4 can be reconstructed from CFT3 primary operators integrated over past or future boundary regions, with kernels given by time-ordered or anti-time-ordered bulk-to-boundary propagators. This rests on showing that the positive and negative energy subspaces of Klein-Gordon solutions are spanned by such propagators (via representation theory and direct computation). The work presents equivalent representations in terms of primaries or shadows, demonstrates that the construction is the AdS analog of flat-space canonical quantization, examines limits yielding plane-wave (Δ→∞) or Carrollian (fixed Δ) bases, and shows an alternative decomposition using principal-series representations of an so(3,1) subalgebra that limits to flat-space conformal primaries.

Significance. If the spanning claim and limit procedures hold, the paper supplies an explicit Lorentzian reconstruction formula that connects AdS bulk operators to boundary data with controlled time orderings and provides a concrete bridge to flat-space quantization and Carrollian structures. The dual use of representation-theoretic arguments together with direct propagator computations is a strength that makes the results more falsifiable and easier to verify.

major comments (1)
  1. [Abstract] Abstract (paragraph beginning 'We show that the positive and negative energy subspaces...'): the central reconstruction formula on Σ_τ relies on the claim that time-ordered bulk-to-boundary propagators span the full positive-energy KG subspace (and anti-time-ordered for negative energy) with respect to the Klein-Gordon inner product. The representation-theoretic argument and direct computations should be expanded to demonstrate completeness for general Δ; without an explicit check that no modes are missing on a constant-time slice, the integral expression over past/future regions may fail to reproduce arbitrary free-field data.
minor comments (2)
  1. [Notation and conventions] Clarify the precise range of Δ for which the time-ordering prescriptions remain well-defined and the propagators are normalizable.
  2. [Flat space limits] In the flat-space limit discussion, specify the order of limits when taking Δ→∞ versus fixed Δ to obtain the plane-wave versus Carrollian bases.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We appreciate the positive assessment of the significance of our results connecting Lorentzian AdS reconstruction to flat-space and Carrollian structures. We address the single major comment below and will revise the manuscript to incorporate an expanded completeness argument.

read point-by-point responses

  1. Referee: [Abstract] Abstract (paragraph beginning 'We show that the positive and negative energy subspaces...'): the central reconstruction formula on Σ_τ relies on the claim that time-ordered bulk-to-boundary propagators span the full positive-energy KG subspace (and anti-time-ordered for negative energy) with respect to the Klein-Gordon inner product. The representation-theoretic argument and direct computations should be expanded to demonstrate completeness for general Δ; without an explicit check that no modes are missing on a constant-time slice, the integral expression over past/future regions may fail to reproduce arbitrary free-field data.

    Authors: We thank the referee for highlighting the need for greater explicitness on this point. The manuscript already contains a representation-theoretic argument (Section 2) establishing that the time-ordered bulk-to-boundary propagators generate the full positive-energy subspace of Klein-Gordon solutions for general Δ, as these kernels correspond to matrix elements in the unitary irreducible representations of SO(3,2) that exhaust the positive-energy sector. Direct computations of the propagators and their action on boundary primaries are given in Section 3, together with verification in various limits. Nevertheless, we agree that an additional explicit check of completeness directly on the constant-time hypersurface Σ_τ would strengthen the presentation and make the reconstruction formula more transparent. In the revised version we will expand Section 3 to include a direct computation of the Klein-Gordon inner product on Σ_τ, demonstrating that the integral over past (or future) boundary regions reproduces arbitrary free-field data for general Δ without missing modes. This addition will not alter the main results or conclusions. revision: yes

Circularity Check

0 steps flagged

Derivations from isometry algebra and direct propagator calculations are independent of target reconstruction

full rationale

The paper establishes the spanning property of positive/negative energy KG subspaces by bulk-to-boundary propagators via representation theory of the AdS isometry algebra plus explicit propagator computations on constant-time slices. The bulk field reconstruction on Σ_τ then follows as a consequence rather than a presupposition. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the core chain; the flat-space limits are likewise obtained by direct asymptotic analysis. This keeps the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The reconstruction rests on standard free-field assumptions in AdS/CFT together with the key spanning property of time-ordered propagators; no new particles or forces are introduced.

free parameters (1)
  • Delta
    Conformal dimension of boundary operators; taken to infinity for plane-wave basis or held fixed for Carrollian basis.
axioms (2)
  • domain assumption Positive and negative energy subspaces of Klein-Gordon solutions are spanned by bulk-to-boundary propagators with appropriate time orderings.
    Invoked in the abstract as the starting point for the reconstruction on Σ_τ.
  • standard math Standard AdS/CFT dictionary relating bulk free scalars to boundary primaries and shadows.
    Background assumption used throughout the reconstruction.

pith-pipeline@v0.9.0 · 5835 in / 1371 out tokens · 44323 ms · 2026-05-20T15:46:25.671214+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

135 extracted references · 135 canonical work pages · 52 internal anchors

  1. [1]

    The Large N Limit of Superconformal Field Theories and Supergravity

    J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2 (1998) 231–252, arXiv:hep-th/9711200

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  2. [2]

    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, arXiv:hep-th/9905111. 75

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  3. [3]

    Gauge Theory Correlators from Non-Critical String Theory

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428 (1998) 105–114, arXiv:hep-th/9802109

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  4. [4]

    Anti De Sitter Space And Holography

    E. Witten, “Anti de Sitter space and holography,” Adv. Theor. Math. Phys. 2 (1998) 253–291, arXiv:hep-th/9802150

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  5. [5]

    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,” JHEP 10 (2008) 091, arXiv:0806.1218 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  6. [6]

    AdS Dynamics from Conformal Field Theory

    T. Banks, M. R. Douglas, G. T. Horowitz, and E. J. Martinec, “AdS dynamics from conformal field theory,” arXiv:hep-th/9808016

    work page internal anchor Pith review Pith/arXiv arXiv

  7. [7]

    Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence

    S. de Haro, S. N. Solodukhin, and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,” Commun. Math. Phys. 217 (2001) 595–622, arXiv:hep-th/0002230

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  8. [8]

    Lecture Notes on Holographic Renormalization

    K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19 (2002) 5849–5876, arXiv:hep-th/0209067

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  9. [9]

    Holographic Derivation of Entanglement Entropy from AdS/CFT

    S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96 (2006) 181602, arXiv:hep-th/0603001

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  10. [10]

    Holographic representation of local bulk operators

    A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev. D 74 (2006) 066009, arXiv:hep-th/0606141

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  11. [11]

    Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT

    D. Harlow and D. Stanford, “Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT,” arXiv:1104.2621 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  12. [12]

    The dS/CFT Correspondence

    A. Strominger, “The dS / CFT correspondence,” JHEP 10 (2001) 034, arXiv:hep-th/0106113

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  13. [13]

    Non-Gaussian features of primordial fluctuations in single field inflationary models

    J. M. Maldacena, “Non-Gaussian features of primordial fluctuations in single field inflationary models,” JHEP 05 (2003) 013, arXiv:astro-ph/0210603

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  14. [14]

    Higher Spin Realization of the dS/CFT Correspondence

    D. Anninos, T. Hartman, and A. Strominger, “Higher Spin Realization of the dS/CFT Correspondence,” Class. Quant. Grav. 34 no. 1, (2017) 015009, arXiv:1108.5735 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  15. [15]

    A holographic reduction of Minkowski space-time

    J. de Boer and S. N. Solodukhin, “A Holographic reduction of Minkowski space-time,” Nucl. Phys. B 665 (2003) 545–593, arXiv:hep-th/0303006

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  16. [16]

    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. D 96 no. 6, (2017) 065026, arXiv:1701.00049 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  17. [17]

    Raclariu,Lectures on Celestial Holography,arXiv:2107.02075

    A.-M. Raclariu, “Lectures on Celestial Holography,” arXiv:2107.02075 [hep-th]

    work page arXiv

  18. [18]

    Lectures on celestial amplitudes,

    S. Pasterski, “Lectures on celestial amplitudes,” Eur. Phys. J. C 81 no. 12, (2021) 1062, arXiv:2108.04801 [hep-th]

    work page arXiv 2021

  19. [19]

    Celestial holography: An asymptotic symmetry perspective,

    L. Donnay, “Celestial holography: An asymptotic symmetry perspective,” Phys. Rept. 1073 (2024) 1–41, arXiv:2310.12922 [hep-th]

    work page arXiv 2024

  20. [20]

    The Carrollian Kaleidoscope

    A. Bagchi, A. Banerjee, P. Dhivakar, S. Mondal, and A. Shukla, “The Carrollian Kaleidoscope,” arXiv:2506.16164 [hep-th] . 76

    work page internal anchor Pith review Pith/arXiv arXiv

  21. [21]

    Gravitational observatories,

    D. Anninos, D. A. Galante, and C. Maneerat, “Gravitational observatories,” JHEP 12 (2023) 024, arXiv:2310.08648 [hep-th]

    work page arXiv 2023

  22. [22]

    Cosmological observatories,

    D. Anninos, D. A. Galante, and C. Maneerat, “Cosmological observatories,” Class. Quant. Grav. 41 no. 16, (2024) 165009, arXiv:2402.04305 [hep-th]

    work page arXiv 2024

  23. [23]

    Gravitational observatories in AdS 4,

    D. Anninos, R. Arias, D. A. Galante, and C. Maneerat, “Gravitational observatories in AdS 4,” JHEP 07 (2025) 234, arXiv:2412.16305 [hep-th]

    work page arXiv 2025

  24. [24]

    Timelike-bounded dS 4 holography from a solvable sector of the T2 deformation,

    E. Silverstein and G. Torroba, “Timelike-bounded dS 4 holography from a solvable sector of the T2 deformation,” JHEP 03 (2025) 156, arXiv:2409.08709 [hep-th]

    work page arXiv 2025

  25. [25]

    The Stretched Horizon Limit,

    D. Anninos, D. A. Galante, S. Georgescu, C. Maneerat, and A. Svesko, “The Stretched Horizon Limit,” arXiv:2512.16738 [hep-th]

    work page arXiv

  26. [26]

    Holography for Cosmology

    P. McFadden and K. Skenderis, “Holography for Cosmology,” Phys. Rev. D 81 (2010) 021301, arXiv:0907.5542 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  27. [27]

    Renormalisation of IR divergences and holography in de Sitter,

    A. Bzowski, P. McFadden, and K. Skenderis, “Renormalisation of IR divergences and holography in de Sitter,” JHEP 05 (2024) 053, arXiv:2312.17316 [hep-th]

    work page arXiv 2024

  28. [28]

    Sleight and M

    C. Sleight and M. Taronna, “Bootstrapping Inflationary Correlators in Mellin Space,” JHEP 02 (2020) 098, arXiv:1907.01143 [hep-th]

    work page arXiv 2020

  29. [29]

    Baumann, C

    D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee, and G. L. Pimentel, “The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization,” SciPost Phys. 11 (2021) 071, arXiv:2005.04234 [hep-th]

    work page arXiv 2021

  30. [30]

    Baumann, D

    D. Baumann, D. Green, A. Joyce, E. Pajer, G. L. Pimentel, C. Sleight, and M. Taronna, “Snowmass White Paper: The Cosmological Bootstrap,” SciPost Phys. Comm. Rep. 2024 (2024) 1, arXiv:2203.08121 [hep-th]

    work page arXiv 2024

  31. [31]

    Cosmological event horizons, thermodynamics, and particle creation,

    G. W. Gibbons and S. W. Hawking, “Cosmological event horizons, thermodynamics, and particle creation,” Phys. Rev. D 15 (May, 1977) 2738–2751. https://link.aps.org/doi/10.1103/PhysRevD.15.2738

    work page doi:10.1103/physrevd.15.2738 1977

  32. [32]

    Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline

    D. Anninos, S. A. Hartnoll, and D. M. Hofman, “Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline,” Class. Quant. Grav. 29 (2012) 075002, arXiv:1109.4942 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  33. [33]

    De Sitter Musings,

    D. Anninos, “De Sitter Musings,” Int. J. Mod. Phys. A 27 (2012) 1230013, arXiv:1205.3855 [hep-th]

    work page arXiv 2012

  34. [34]

    Aspects of the BMS/CFT correspondence

    G. Barnich and C. Troessaert, “Aspects of the BMS/CFT correspondence,” JHEP 05 (2010) 062, arXiv:1001.1541 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  35. [35]

    BMS supertranslations and Weinberg's soft graviton theorem

    T. He, V. Lysov, P. Mitra, and A. Strominger, “BMS supertranslations and Weinberg’s soft graviton theorem,” JHEP 05 (2015) 151, arXiv:1401.7026 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  36. [36]

    Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix

    D. Kapec, V. Lysov, S. Pasterski, and A. Strominger, “Semiclassical Virasoro symmetry of the quantum gravity S-matrix,” JHEP 08 (2014) 058, arXiv:1406.3312 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  37. [37]

    A 2D Stress Tensor for 4D Gravity

    D. Kapec, P. Mitra, A.-M. Raclariu, and A. Strominger, “2D Stress Tensor for 4D Gravity,” Phys. Rev. Lett. 119 no. 12, (2017) 121601, arXiv:1609.00282 [hep-th] . 77

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  38. [38]

    A Conformal Basis for Flat Space Amplitudes

    S. Pasterski and S.-H. Shao, “Conformal basis for flat space amplitudes,” Phys. Rev. D 96 no. 6, (2017) 065022, arXiv:1705.01027 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  39. [39]

    The BMS/GCA correspondence

    A. Bagchi, “Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories,” Phys. Rev. Lett. 105 (2010) 171601, arXiv:1006.3354 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  40. [40]

    Flat Holography: Aspects of the dual field theory

    A. Bagchi, R. Basu, A. Kakkar, and A. Mehra, “Flat Holography: Aspects of the dual field theory,” JHEP 12 (2016) 147, arXiv:1609.06203 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  41. [41]

    Donnay, A

    L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, “Bridging Carrollian and celestial holography,” Phys. Rev. D 107 no. 12, (2023) 126027, arXiv:2212.12553 [hep-th]

    work page arXiv 2023

  42. [42]

    Holographic symmetry algebras for gauge theory and gravity,

    A. Guevara, E. Himwich, M. Pate, and A. Strominger, “Holographic symmetry algebras for gauge theory and gravity,” JHEP 11 (2021) 152, arXiv:2103.03961 [hep-th]

    work page arXiv 2021

  43. [43]

    w1+∞ Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries,

    A. Strominger, “ w1+∞ Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries,” Phys. Rev. Lett. 127 no. 22, (2021) 221601, arXiv:2105.14346 [hep-th]

    work page arXiv 2021

  44. [44]

    Higher spin dynamics in gravity and w1+ ∞ celestial symmetries,

    L. Freidel, D. Pranzetti, and A.-M. Raclariu, “Higher spin dynamics in gravity and w1+ ∞ celestial symmetries,” Phys. Rev. D 106 no. 8, (2022) 086013, arXiv:2112.15573 [hep-th]

    work page arXiv 2022

  45. [45]

    Celestial w1+∞ Symmetries from Twistor Space,

    T. Adamo, L. Mason, and A. Sharma, “Celestial w1+∞ Symmetries from Twistor Space,” SIGMA 18 (2022) 016, arXiv:2110.06066 [hep-th]

    work page arXiv 2022

  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 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  47. [47]

    Associativity is enough: an all-orders 2d chiral algebra for 4d form factors,

    V. E. Fern´ andez and N. M. Paquette, “Associativity is enough: an all-orders 2d chiral algebra for 4d form factors,” Class. Quant. Grav. 42 no. 18, (2025) 185005, arXiv:2412.17168 [hep-th]

    work page arXiv 2025

  48. [48]

    Form factors of $\mathscr{N}=4$ self-dual Yang-Mills from the chiral algebra bootstrap

    J. Charanya, A. Morales, and N. M. Paquette, “Form factors of N = 4 self-dual Yang-Mills from the chiral algebra bootstrap,” arXiv:2604.21015 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  49. [49]

    Holography in the Flat Space Limit

    L. Susskind, “Holography in the flat space limit,” AIP Conf. Proc. 493 no. 1, (1999) 98–112, arXiv:hep-th/9901079

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  50. [50]

    Flat-space scattering and bulk locality in the AdS/CFT correspondence

    S. B. Giddings, “Flat space scattering and bulk locality in the AdS/CFT correspondence,” Phys. Rev. D 61 (2000) 106008, arXiv:hep-th/9907129

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  51. [51]

    The boundary S-matrix and the AdS to CFT dictionary

    S. B. Giddings, “The Boundary S matrix and the AdS to CFT dictionary,” Phys. Rev. Lett. 83 (1999) 2707–2710, arXiv:hep-th/9903048

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  52. [52]

    Scattering States in AdS/CFT

    A. L. Fitzpatrick and J. Kaplan, “Scattering States in AdS/CFT,” arXiv:1104.2597 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  53. [53]

    New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators

    S. Raju, “New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators,” Phys. Rev. D 85 (2012) 126009, arXiv:1201.6449 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  54. [54]

    Looking for a bulk point

    J. Maldacena, D. Simmons-Duffin, and A. Zhiboedov, “Looking for a bulk point,” JHEP 01 (2017) 013, arXiv:1509.03612 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  55. [55]

    Landau diagrams in AdS and S-matrices from conformal correlators,

    S. Komatsu, M. F. Paulos, B. C. Van Rees, and X. Zhao, “Landau diagrams in AdS and S-matrices from conformal correlators,” JHEP 11 (2020) 046, arXiv:2007.13745 [hep-th] . 78

    work page arXiv 2020

  56. [56]

    Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms,

    B. C. van Rees and X. Zhao, “Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms,” Phys. Rev. Lett. 130 no. 19, (2023) 191601, arXiv:2210.15683 [hep-th]

    work page arXiv 2023

  57. [57]

    Flat space spinning massive amplitudes from momentum space CFT,

    R. Marotta, K. Skenderis, and M. Verma, “Flat space spinning massive amplitudes from momentum space CFT,” JHEP 08 (2024) 226, arXiv:2406.06447 [hep-th]

    work page arXiv 2024

  58. [58]

    Writing CFT correlation functions as AdS scattering amplitudes

    J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP 03 (2011) 025, arXiv:1011.1485 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  59. [59]

    A Natural Language for AdS/CFT Correlators

    A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju, and B. C. van Rees, “A Natural Language for AdS/CFT Correlators,” JHEP 11 (2011) 095, arXiv:1107.1499 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  60. [60]

    Notes on flat-space limit of AdS/CFT,

    Y.-Z. Li, “Notes on flat-space limit of AdS/CFT,” JHEP 09 (2021) 027, arXiv:2106.04606 [hep-th]

    work page arXiv 2021

  61. [61]

    Eikonal approximation in celestial CFT,

    L. P. de Gioia and A.-M. Raclariu, “Eikonal approximation in celestial CFT,” JHEP 03 (2023) 030, arXiv:2206.10547 [hep-th]

    work page arXiv 2023

  62. [62]

    Bagchi, P

    A. Bagchi, P. Dhivakar, and S. Dutta, “AdS Witten diagrams to Carrollian correlators,” JHEP 04 (2023) 135, arXiv:2303.07388 [hep-th]

    work page arXiv 2023

  63. [63]

    Celestial amplitudes from conformal correlators with bulk-point kinematics,

    L. P. de Gioia and A.-M. Raclariu, “Celestial amplitudes from conformal correlators with bulk-point kinematics,” arXiv:2405.07972 [hep-th]

    work page arXiv

  64. [64]

    Carrollian amplitudes from holographic correlators,

    L. F. Alday, M. Nocchi, R. Ruzziconi, and A. Yelleshpur Srikant, “Carrollian amplitudes from holographic correlators,” JHEP 03 (2025) 158, arXiv:2406.19343 [hep-th]

    work page arXiv 2025

  65. [65]

    Towards a flat space Carrollian hologram from AdS 4/CFT3,

    A. Lipstein, R. Ruzziconi, and A. Yelleshpur Srikant, “Towards a flat space Carrollian hologram from AdS 4/CFT3,” JHEP 06 (2025) 073, arXiv:2504.10291 [hep-th]

    work page arXiv 2025

  66. [66]

    From celestial correlators to AdS, and back,

    L. Iacobacci, C. Sleight, and M. Taronna, “From celestial correlators to AdS, and back,” JHEP 06 (2023) 053, arXiv:2208.01629 [hep-th]

    work page arXiv 2023

  67. [67]

    Celestial Holography Revisited,

    C. Sleight and M. Taronna, “Celestial Holography Revisited,” Phys. Rev. Lett. 133 no. 24, (2024) 241601, arXiv:2301.01810 [hep-th]

    work page arXiv 2024

  68. [68]

    Celestial leaf amplitudes,

    W. Melton, A. Sharma, and A. Strominger, “Celestial leaf amplitudes,” JHEP 07 (2024) 132, arXiv:2312.07820 [hep-th]

    work page arXiv 2024

  69. [69]

    Quantum Fields on Time-Periodic AdS 3/Z,

    W. Melton, A. Strominger, and T. Wang, “Quantum Fields on Time-Periodic AdS 3/Z,” arXiv:2510.15036 [hep-th]

    work page arXiv

  70. [70]

    Celestial sector in CFT: Conformally soft symmetries,

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

    work page arXiv 2024

  71. [71]

    Infinite towers of 2d symmetry algebras from Carrollian limit of 3d CFT,

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

    work page arXiv

  72. [72]

    Aspects of the bulk flat space limit in AdS/CFT,

    D. Berenstein and J. Simon, “Aspects of the bulk flat space limit in AdS/CFT,” arXiv:2510.23697 [hep-th]

    work page arXiv

  73. [73]

    Weinberg, The Quantum theory of fields

    S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations . Cambridge University Press, 6, 2005. 79

    work page 2005

  74. [74]

    Null Infinity and Unitary Representation of The Poincare Group

    S. Banerjee, “Null Infinity and Unitary Representation of The Poincare Group,” JHEP 01 (2019) 205, arXiv:1801.10171 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  75. [75]

    Golden oldie: Null hypersurface initial data for classical fields of arbitrary spin and for general relativity,

    R. Penrose, “Golden oldie: Null hypersurface initial data for classical fields of arbitrary spin and for general relativity,” General Relativity and Gravitation 12 no. 3, (1980) 225–264. https://doi.org/10.1007/BF00756234

    work page doi:10.1007/bf00756234 1980

  76. [76]

    Heaven and Its Properties,

    E. T. Newman, “Heaven and Its Properties,” Gen. Rel. Grav. 7 (1976) 107–111

    work page 1976

  77. [77]

    A discrete basis for celestial holography,

    L. Freidel, D. Pranzetti, and A.-M. Raclariu, “A discrete basis for celestial holography,” JHEP 02 (2024) 176, arXiv:2212.12469 [hep-th]

    work page arXiv 2024

  78. [78]

    Goldilocks modes and the three scattering bases,

    L. Donnay, S. Pasterski, and A. Puhm, “Goldilocks modes and the three scattering bases,” JHEP 06 (2022) 124, arXiv:2202.11127 [hep-th]

    work page arXiv 2022

  79. [79]

    Celestial Conformal Primaries in Effective Field Theories,

    P. Mitra, “Celestial Conformal Primaries in Effective Field Theories,” arXiv:2402.09256 [hep-th]

    work page arXiv

  80. [80]

    Shadows and soft exchange in celestial CFT,

    D. Kapec and P. Mitra, “Shadows and soft exchange in celestial CFT,” Phys. Rev. D 105 no. 2, (2022) 026009, arXiv:2109.00073 [hep-th]

    work page arXiv 2022

Showing first 80 references.