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The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity

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Pith's one-line read This paper claims that quadratic-curvature corrections make the celestial eikonal amplitude meromorphic in the conformal dimension $\gamma$, with an infinite tower of simple poles, and that shadowing one operator yields computable OPE…

desk verdict New celestial eikonal/OPE work for quadratic gravity, but a specific error in the phase linearization makes the central result unsound as written. read the letter →

arxiv 2505.02899 v2 pith:YSHZI3UI submitted 2025-05-05 hep-th gr-qcmath-phmath.MP

Arpan Bhattacharyya , Saptaswa Ghosh , Sounak Pal This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP
keywords celestialamplitudesquadraticgravityeikonalapproximationconformalblockexpansionOPEinversionformulashadowtransformAppellhypergeometricfunctionCarrollianamplitude
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 takes the celestial holography program, which recasts flat-space scattering amplitudes as correlators of a two-dimensional conformal field theory on the celestial sphere, and asks what happens when Einstein gravity is extended by quadratic curvature terms with Wilson coefficients $\alpha$ and $\beta$. It claims that in the eikonal (high-energy, small-angle) limit these corrections remove a cancellation: the $s$- and $u$-channel contributions, which cancel in general relativity, remain nonzero, so the Mellin-transformed amplitude acquires a meromorphic structure in the conformal dimension $\gamma$ instead of the delta-function distributional form of GR. The paper further extracts the operator product expansion data of the resulting celestial conformal field theory by shadowing one external operator, decomposing the correlator into conformal blocks, and using the Burchnall-Chaundy expansion and the Euclidean OPE inversion formula. A sympathetic reader would care because analytic celestial amplitudes are rare in gravitational theories, and the machinery used here gives a route to OPE data that does not rely on the collinear limit.

What carries the argument

The argument runs through a chain: the eikonal phase built from the Born amplitude in quadratic gravity, whose contact term is a Dirac delta handled by an analytic-linearization prescription; the Mellin transform to the conformal primary basis; a shadow transform on one external operator to relax the planarity delta function; the Burchnall-Chaundy expansion of the Appell $F_1$ function into products of Gauss hypergeometric functions, which identifies the scalar-exchange conformal blocks; and the Euclidean OPE inversion formula, whose residues at towers of poles in the partial-wave coefficient give OPE coefficients for general spin $J$. Each step converts a piece of the flat-space amplitude into a standard two-dimensional CFT object, and the factorization of the $\omega$-integral from the cross-ratio dependence in the EFT correction is what makes the same OPE analysis reach the non-perturbative eikonal amplitude.

What would settle it

Compute the two-loop ladder and cross-ladder diagrams for massless scalar scattering in quadratic gravity in the Regge limit: if the sum does not exponentiate into the phase $e^{i\chi}$ with $\chi$ built from the Born amplitude as in Eq. (31), then the phase-dressed eikonal celestial amplitude and its pole structure do not follow, a step the paper identifies as missing.

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Extended reading notes

Core claim

For non-zero $\alpha$ and $\beta$, the phase-dressed eikonal celestial amplitude in quadratic gravity is meromorphic in $\gamma$, with simple poles at $\gamma = -2(n+1)$ in the infrared regime, in contrast to the distributional GR result; the shadowed correlator admits a conformal block expansion whose OPE coefficients can be computed, including spinning exchanges, from residues of the analytically continued partial-wave coefficients. The paper also derives a dispersion relation for the eikonal amplitude that encodes the massive poles $\omega' = \pm \kappa/\alpha, \pm \kappa/(2\beta)$ coming from the quadratic corrections, and shows that the associated Carrollian amplitude has an infrared pole shifted by the EFT couplings. The key structural claim is that the eikonal amplitude remains a product of a Born amplitude and a phase, so the improved analytic behavior of the Born amplitude survives phase dressing.

Load-bearing premise

The load-bearing premise is that eikonal exponentiation remains valid in quadratic gravity, together with the analytic-linearization prescription that defines the exponential of the Dirac-delta contact term; the paper explicitly notes that a full demonstration would require explicit loop-level diagram computation.

Editorial extensions

If this is right

  • If the central claim holds, the celestial correlator of quadratic gravity is no longer a distribution: it has isolated poles in $\gamma$, so standard CFT techniques apply without an extra regularization prescription.
  • The OPE coefficients obtained from the shadowed correlator give concrete CFT data for a gravitational theory beyond Einstein gravity, including spinning exchanges that the Burchnall-Chaundy expansion alone misses.
  • The dispersion relation for the phase-dressed eikonal amplitude encodes the massive graviton poles of the EFT, so the celestial amplitude remembers the massive modes introduced by the quadratic curvature terms.
  • Because the $\omega$-integral factorizes from the cross-ratio dependence in the EFT correction, the OPE analysis extends from the Born amplitude to the full eikonal amplitude, at least for the EFT part.
  • The shift of the infrared pole in the Carrollian amplitude connects the EFT corrections to the boost-invariance structure of flat-space holography.

Reading between the lines

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

  • If eikonal exponentiation is confirmed at loop level, the same meromorphicity mechanism should extend to any higher-derivative EFT whose Born amplitude has a finite number of massive poles, making celestial OPE data computable across a whole class of theories.
  • The simple-pole infrared structure at $\gamma = -2(n+1)$, rather than the higher-order poles of GR, may be a direct signature of the massive spin-2 mode; a testable prediction is that the OPE coefficient residues carry the $\alpha,\beta$ dependence found in the paper's Eq. (89).
  • An exact evaluation of the OPE inversion integral, without the $\rho \ll 1$ approximation used to simplify the Appell function, could settle whether the discrepancy between the Burchnall-Chaundy and inversion results at large $\text{Im}\,\Delta_O$ is an artifact of the approximation.
  • The Carrollian infrared-pole shift could serve as a sharp diagnostic: since boost invariance protects that pole, a fully non-perturbative treatment that preserved the shift would support the physical relevance of the EFT corrections to flat-space holography.
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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

4 major / 5 minor

Summary. The manuscript studies celestial holography for a quadratic higher-derivative gravity EFT with action (11). It computes the Born-level eikonal amplitude, dresses it with an eikonal phase that contains a Dirac-delta contact term, performs a Mellin transform to obtain a celestial amplitude, derives a dispersion relation for the phase-dressed amplitude, constructs shadowed four-point correlators in terms of Appell F1 functions, extracts OPE coefficients using the Burchnall-Chaundy expansion and the Euclidean OPE inversion formula, and finally gives a Carrollian amplitude. The advertised main results are: (i) in quadratic gravity the s- and u-channel contributions no longer cancel in the eikonal limit; (ii) the phase-dressed celestial eikonal amplitude is meromorphic in gamma with an infinite set of simple poles, in contrast to the distributional GR result; and (iii) OPE coefficients can be extracted from the shadowed Born and eikonal correlators.

Significance. The question addressed is worthwhile: celestial amplitudes in UV-incomplete gravitational theories are usually distributional or divergent, and higher-derivative EFTs provide a natural laboratory for studying whether improved UV behaviour leads to meromorphic celestial amplitudes. If the eikonal construction were valid, the non-cancellation of s/u channels and the pole structure would be a concrete and interesting example. The paper is self-contained in the sense that alpha and beta are input Wilson coefficients and no fitted value is fed back as a prediction; the Born-level Mellin integrals and the Burchnall-Chaundy manipulation of the Appell function are useful technical contributions. However, as detailed in the major comments, the central eikonal result depends on an internally inconsistent treatment of exp(delta) and on an explicitly acknowledged but unproven exponentiation assumption, so the advertised meromorphic celestial eikonal amplitude and the subsequent OPE analysis are not established.

major comments (4)
  1. [§3.2, Eq. (38)] The passage from Eq. (36) to Eq. (38) replaces exp(c delta^(2)(x_perp)) with 1 + (e-1) c delta^(2)(x_perp), where c = 2*pi*i*G*eMEFT_Born(s)/E_p. This does not follow from the Analytic Linearization definition in Eq. (34). For f(x)=exp(c x), Eq. (34) gives, if idempotence of delta is used, 1 + (e^c - 1) delta, not 1 + (e-1) c delta; the naive Taylor expansion gives 1 + c delta plus undefined higher powers. The factor (e-1) is not justified unless c=1, which is not the case. This spurious factor propagates into the eikonal amplitude (41), the Mellin integrals (42)-(45), the pole analysis, and the dispersion relation (61). Since the shadowed correlator and OPE analysis in Section 4 take this amplitude as input, this is a load-bearing error in the central claim.
  2. [§3.2, exponentiation assumption] The paper explicitly states that ``a full demonstration of exponentiation in quadratic gravity would require explicit computation of loop-level diagrams... We intend to explore this in future work.'' The IR-universality argument in Section 3.2 and the reference to [59] are plausible but do not establish validity of phase dressing for the massive spin-2 and spin-0 modes that appear in the propagator (12). Because the phase-dressed eikonal amplitude (36)-(41) is the starting point for the dispersion relation, the celestial eikonal amplitude, and the OPE analysis, this is a load-bearing assumption rather than a derived result.
  3. [§4.2-4.3, Eq. (89)] After shadowing, operator 2 has conformal dimension 2-Delta_2, as stated after Eq. (63). Setting all external conformal dimensions equal to Delta_O in Eq. (89) and in the block parameters a,b below Eq. (83) is therefore inconsistent unless Delta_O=1. With Delta_2=Delta_O, the shadowed operator has dimension 2-Delta_O, which changes the value of gamma and the block arguments. Consequently, the scalar-exchange OPE coefficient f^2_OOO in Eq. (89) and the comparison in Fig. 5 are not the equal-dimension limit of the shadowed correlator but rather a different correlator.
  4. [§4.3, Eqs. (95)-(100)] The Euclidean OPE inversion is performed under uncontrolled approximations: rho_w, rho_bar_w << 1, the hypergeometric functions are set to 1, and the Appell function is approximated by the expression in Eq. (96). The residues in Eqs. (99)-(100) are therefore approximate, and the paper does not provide an error estimate. The discrepancy already visible in Fig. 5 at moderate Im(Delta_O) shows that the extracted OPE coefficients are indicative rather than derived, which matters because the abstract presents these coefficients as computed results.
minor comments (5)
  1. [Throughout] The word ``ultrablack'' is used where ``ultraviolet'' or ``UV'' is meant, e.g., in Section 3.3 and the conclusion; please correct this typo.
  2. [Eq. (23)] The notation delta(i(gamma+2)) is unusual for a Dirac delta of an imaginary argument; please define it explicitly, presumably as a delta function in gamma with a Jacobian factor.
  3. [Eq. (24)] The expression for delta_1(alpha,beta|gamma) is hard to parse: ``beta^(-gamma/2-1) - 2^(gamma/2+3) alpha^(-gamma/2-1)'' appears to have ambiguous grouping. Please rewrite this equation with clear parentheses.
  4. [§4.1, Eq. (67)] The GR part of the shadowed eikonal correlator is written down but not evaluated, and the paper then switches to the Born amplitude for the OPE analysis. The scope of the OPE claims should be stated precisely at the start of Section 4, because the eikonal OPE statement is only established for the EFT-correction part and only formally.
  5. [Fig. 5 and Eq. (41)] The notation with the circled plus sign in Eq. (41) is nonstandard and should be defined. In Fig. 5, please state explicitly the values of alpha, beta (or the normalization factor) used in the comparison, and indicate whether the discrepancy at larger Im(Delta_O) is within the expected size of the approximations in Eq. (96).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; alpha and beta are free inputs, the Born amplitude is computed from the propagator, and the OPE data are extracted from the resulting celestial amplitude rather than used to construct it.

full rationale

The paper's derivation chain is input-to-output: the action (11) and propagator (12) fix the Born amplitude (21); the eikonal phase (31) is computed from that amplitude; the Mellin transform (42) converts it to a celestial amplitude; and Section 4 extracts OPE coefficients by conformal-block and OPE-inversion techniques from the resulting celestial amplitude. No fitted parameter is fed back as a prediction, and no central definition is stated in terms of the claimed output. The self-citations present ([9] and [42]) appear only in introductory or contextual lists and are not load-bearing; in particular, the eikonal-exponentiation premise is justified by standard external references and is explicitly flagged as an assumption ('a full demonstration of exponentiation in quadratic gravity would require explicit computation of loop-level diagrams... We intend to explore this in future work'), which is a validity caveat rather than a circular step. The questionable replacement in Eq. (38), where exp(c delta) is replaced by 1+(e-1)c delta, is a mathematical-consistency issue in applying the externally cited analytic-linearization definition (34), not a case of the derivation's output being equivalent to its input. Likewise, the OPE coefficients are by construction proportional to the input amplitude's coefficient delta_1, but that is the standard extraction of CFT data from a known correlator, not a circular prediction. I therefore find no circularity.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

No numbers are fitted to data: alpha and beta are input Wilson coefficients of the quadratic-gravity action and the regulators mu, epsilon are not fitted. The load-bearing assumptions are the unproved eikonal exponentiation in quadratic gravity, the formal treatment of functions of the Dirac delta, and the shadow-transform framework. No new particles or entities are introduced beyond the known massive spin-2 ghost of quadratic gravity.

assumptions (3)
  • domain assumption Eikonal exponentiation holds for quadratic gravity, so the full amplitude is a Born amplitude times a phase.
    Section 3.2 states the authors 'believe' it, cite IR universality and [59], and explicitly acknowledge the absence of a loop-level demonstration. The eikonal amplitude and dispersion relation depend on it.
  • ad hoc to paper Functions of the Dirac delta can be defined by analytic linearization and smearing, so exp(i chi) with a delta(x_perp) contact term has a meaningful distributional value.
    Section 3.2 digression imports the construction from [61,62]; it is formal and the smearing regulator epsilon controls the result. This is needed to obtain the phase-dressed EFT amplitude Eq. 40.
  • domain assumption The shadow transform makes z and z-bar independent so standard Euclidean conformal block techniques apply.
    Sections 4.1-4.3 rely on [29,30] to replace delta(|z-z-bar|) with a two-dimensional integral and to use OPE inversion. This is a background assumption of CCFT, not proved here.

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Pith. "Pith review of The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity." pith.science (2026). https://pith.science/paper/YSHZI3UI

@misc{pith2026250502899,
  author       = {Pith},
  title        = {Pith review of: The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YSHZI3UI}},
  note         = {Machine review of arXiv:2505.02899}
}
abstract

In this paper, we compute the celestial amplitude arising from higher curvature corrections to Einstein gravity, incorporating phase dressing. The inclusion of such corrections leads to effective modifications of the theory's ultraviolet (UV) behaviour. In the eikonal limit, we find that, in contrast to Einstein's gravity, where the $u$ and $s$-channel contributions cancel, these contributions remain non-vanishing in the presence of higher curvature terms. We examine the analytic structure of the resulting amplitude and derive a dispersion relation for the phase-dressed eikonal amplitude in quadratic gravity. Furthermore, we investigate the celestial conformal block expansion of the Mellin-transformed conformal shadow amplitude within the framework of celestial conformal field theory (CCFT). As a consequence, we compute the corresponding operator product expansion (OPE) coefficients using the Burchnall-Chaundy expansion. In addition, we evaluate the OPE via the Euclidean OPE inversion formula across various kinematic channels and comment on its applicability and implications. Finally, we briefly explore the Carrollian amplitude associated with the corresponding quadratic EFT.

Figures

Figures reproduced from arXiv: 2505.02899 by the authors.

Figure 1
Figure 1. Figure describing the celestial description of conformal correlator (right) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure depicting the regime of validity for Mellin transformed amplitude(s) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure describing the s, t, u-channel diagram respectively, relevant for our computation Before proceeding to the main discussion, we begin by outlining several foundational aspects of quadratic effective field theories (EFTs) of gravity. It is well understood that quantum correc￾tions to Einstein gravity generically induce higher-derivative terms, including those quadratic in the curvature, such as R 2 . This natur… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Figure depicting the chosen contour for dispersion relation in the complex [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]
Figure 5
Figure 5. Figure 5: Plot depicting the matching for extraction of OPE coefficient using BC [PITH_FULL_IMAGE:figures/full_fig_p031_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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Reference graph

Works this paper leans on

78 extracted references · 17 canonical work pages · cited by 3 Pith papers

  1. [59]

    Di Vecchia, C

    P . Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, The gravitational eikonal: From particle, string and brane collisions to black-hole encounters, Phys. Rept. 1083, 1 (2024), doi:10.1016 /j.physrep.2024.06.002, 2306.16488

    arXiv 2024

  2. [1]

    J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2, 231 (1998), doi:10.4310 /ATMP .1998.v2.n2.a1, hep-th/9711200

    arXiv 1998

  3. [2]

    Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07, 152 (2014), doi:10.1007/JHEP07(2014)152, 1312.2229

    A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07, 152 (2014), doi:10.1007/JHEP07(2014)152, 1312.2229

    arXiv 2014

  4. [3]

    Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, ISBN 978-0-691-17973-5 (2017), 1703.05448

    A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, ISBN 978-0-691-17973-5 (2017), 1703.05448

    arXiv 2017

  5. [4]

    Pasterski, S.-H

    S. Pasterski, S.-H. Shao and A. Strominger, Gluon Amplitudes as 2d Conformal Correlators, Phys. Rev. D 96(8), 085006 (2017), doi:10.1103/PhysRevD.96.085006, 1706.03917

    arXiv 2017

  6. [5]

    Pasterski, M

    S. Pasterski, M. Pate and A.-M. Raclariu, Celestial Holography, In Snowmass 2021 (2021), 2111.11392

    arXiv 2021

  7. [6]

    Donnay , S

    L. Donnay , S. Pasterski and A. Puhm,Asymptotic Symmetries and Celestial CFT, JHEP 09, 176 (2020), doi:10.1007 /JHEP09(2020)176, 2005.08990

    arXiv 2020

  8. [7]

    T . He, V . Lysov, P . Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05, 151 (2015), doi:10.1007/JHEP05(2015)151, 1401.7026

    arXiv 2015

Show all 78 references
  1. [8]

    Adamo, L

    T . Adamo, L. Mason and A. Sharma,Celestial amplitudes and conformal soft theorems, Class. Quant. Grav. 36(20), 205018 (2019), doi:10.1088 /1361-6382/ab42ce, 1905.09224. 36 SciPost Physics Submission

    2019 arXiv

  2. [9]

    Banerjee, S

    S. Banerjee, S. Ghosh and R. Gonzo, BMS symmetry of celestial OPE, JHEP 04, 130 (2020), doi:10.1007 /JHEP04(2020)130, 2002.00975

    2020 arXiv

  3. [10]

    H. A. González, A. Puhm and F . Rojas,Loop corrections to celestial amplitudes, Phys. Rev. D102(12), 126027 (2020), doi:10.1103 /PhysRevD.102.126027, 2009.07290

    2020 arXiv

  4. [11]

    Pasterski, A

    S. Pasterski, A. Puhm and E. Trevisani, Celestial diamonds: conformal multiplets in celestial CFT, JHEP 11, 072 (2021), doi:10.1007/JHEP11(2021)072, 2105.03516

    2021 arXiv

  5. [12]

    Gonzo, T

    R. Gonzo, T . McLoughlin and A. Puhm, Celestial holography on Kerr-Schild backgrounds, JHEP 10, 073 (2022), doi:10.1007/JHEP10(2022)073, 2207.13719

    2022 arXiv

  6. [13]

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

    A. Strominger, w1+∞ Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries, Phys. Rev. Lett.127(22), 221601 (2021), doi:10.1103 /PhysRevLett.127.221601, 2105.14346

    2021 arXiv

  7. [14]

    Pasterski, S.-H

    S. Pasterski, S.-H. Shao and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96(6), 065026 (2017), doi:10.1103 /PhysRevD.96.065026, 1701.00049

    2017 arXiv

  8. [15]

    Osborn, Conformal Blocks for Arbitrary Spins in Two Dimensions, Phys

    H. Osborn, Conformal Blocks for Arbitrary Spins in Two Dimensions, Phys. Lett. B 718, 169 (2012), doi:10.1016 /j.physletb.2012.09.045, 1205.1941

    2012 arXiv

  9. [16]

    Poland, S

    D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory , Numerical Techniques, and Applications, Rev. Mod. Phys. 91, 015002 (2019), doi:10.1103 /RevModPhys.91.015002, 1805.04405

    2019 arXiv

  10. [17]

    H. T . Lam and S.-H. Shao, Conformal Basis, Optical Theorem, and the Bulk Point Singularity, Phys. Rev. D 98(2), 025020 (2018), doi:10.1103 /PhysRevD.98.025020, 1711.06138

    2018 arXiv

  11. [18]

    Nandan, A

    D. Nandan, A. Schreiber, A. Volovich and M. Zlotnikov, Celestial Amplitudes: Conformal Partial Waves and Soft Limits, JHEP 10, 018 (2019), doi:10.1007/JHEP10(2019)018, 1904.10940

    2019 arXiv

  12. [19]

    Y. T . A. Law and M. Zlotnikov,Relativistic partial waves for celestial amplitudes, JHEP 11, 149 (2020), doi:10.1007 /JHEP11(2020)149, 2008.02331

    2020 arXiv

  13. [20]

    W . Fan, A. Fotopoulos, S. Stieberger, T . R. Taylor and B. Zhu, Conformal blocks from celestial gluon amplitudes, JHEP 05, 170 (2021), doi:10.1007/JHEP05(2021)170, 2103.04420

    2021 arXiv

  14. [21]

    W . Fan, A. Fotopoulos, S. Stieberger, T . R. Taylor and B. Zhu, Elements of celestial conformal field theory, JHEP 08, 213 (2022), doi:10.1007/JHEP08(2022)213, 2202.08288

    2022 arXiv

  15. [22]

    W . Fan, A. Fotopoulos, S. Stieberger, T . R. Taylor and B. Zhu, Celestial Yang-Mills amplitudes and D = 4 conformal blocks, JHEP 09, 182 (2022), doi:10.1007/JHEP09(2022)182, 2206.08979

    2022 arXiv

  16. [23]

    Atanasov, W

    A. Atanasov, W . Melton, A.-M. Raclariu and A. Strominger, Conformal block expansion in celestial CFT, Phys. Rev. D 104(12), 126033 (2021), doi:10.1103/PhysRevD.104.126033, 2104.13432. 37 SciPost Physics Submission

    2021 arXiv

  17. [24]

    S. De, Y. Hu, A. Yelleshpur Srikant and A. Volovich, Correlators of four light-ray operators in CCFT, JHEP 10, 170 (2022), doi:10.1007/JHEP10(2022)170, 2206.08875

    2022 arXiv

  18. [25]

    García-Sepúlveda, A

    D. García-Sepúlveda, A. Guevara, J. Kulp and J. Wu, Notes on resonances and unitarity from celestial amplitudes, JHEP 09, 245 (2022), doi:10.1007/JHEP09(2022)245, 2205.14633

    2022 arXiv

  19. [26]

    Banerjee, H

    S. Banerjee, H. Kulkarni and P . Paul,Celestial OPE in self-dual gravity, Phys. Rev. D 109(8), 086017 (2024), doi:10.1103 /PhysRevD.109.086017, 2311.06485

    2024 arXiv

  20. [27]

    Ferrara and G

    S. Ferrara and G. Parisi, Conformal covariant correlation functions, Nuclear Physics B 42, 281 (1972), doi:https: //doi.org/10.1016/0550-3213(72)90480-4

    1972 doi

  21. [28]

    Ferrara, A

    S. Ferrara, A. F . Grillo, G. Parisi and R. Gatto, Covariant expansion of the conformal four-point function, Nucl. Phys. B 49, 77 (1972), doi:10.1016/0550-3213(73)90467-7, [Erratum: Nucl.Phys.B 53, 643–643 (1973)]

    1972 doi

  22. [29]

    Simmons-Duffin, Projectors, Shadows, and Conformal Blocks, JHEP 04, 146 (2014), doi:10.1007/JHEP04(2014)146, 1204.3894

    D. Simmons-Duffin, Projectors, Shadows, and Conformal Blocks, JHEP 04, 146 (2014), doi:10.1007/JHEP04(2014)146, 1204.3894

    2014 arXiv

  23. [30]

    Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09, 078 (2017), doi:10.1007/JHEP09(2017)078, 1703.00278

    S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09, 078 (2017), doi:10.1007/JHEP09(2017)078, 1703.00278

    2017 arXiv

  24. [31]

    Simmons-Duffin, D

    D. Simmons-Duffin, D. Stanford and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, JHEP 07, 085 (2018), doi:10.1007/JHEP07(2018)085, 1711.03816

    2018 arXiv

  25. [32]

    Mazáˇc, A Crossing-Symmetric OPE Inversion Formula, JHEP 06, 082 (2019), doi:10.1007/JHEP06(2019)082, 1812.02254

    D. Mazáˇc, A Crossing-Symmetric OPE Inversion Formula, JHEP 06, 082 (2019), doi:10.1007/JHEP06(2019)082, 1812.02254

    2019 arXiv

  26. [33]

    Arkani-Hamed, M

    N. Arkani-Hamed, M. Pate, A.-M. Raclariu and A. Strominger, Celestial amplitudes from UV to IR, JHEP 08, 062 (2021), doi:10.1007/JHEP08(2021)062, 2012.04208

    2021 arXiv

  27. [34]

    Stieberger and T

    S. Stieberger and T . R. Taylor,Strings on Celestial Sphere, Nucl. Phys. B 935, 388 (2018), doi:10.1016 /j.nuclphysb.2018.08.019, 1806.05688

    2018 arXiv

  28. [35]

    Chang, Y.-t

    C.-M. Chang, Y.-t. Huang, Z.-X. Huang and W . Li, Bulk locality from the celestial amplitude, SciPost Phys. 12(5), 176 (2022), doi:10.21468/SciPostPhys.12.5.176, 2106.11948

    2022 arXiv

  29. [36]

    Donnay , G

    L. Donnay , G. Giribet, H. González, A. Puhm and F . Rojas, Celestial open strings at one-loop, JHEP 10, 047 (2023), doi:10.1007/JHEP10(2023)047, 2307.03551

    2023 arXiv

  30. [37]

    Casali, W

    E. Casali, W . Melton and A. Strominger,Celestial amplitudes as AdS-Witten diagrams, JHEP 11, 140 (2022), doi:10.1007 /JHEP11(2022)140, 2204.10249

    2022 arXiv

  31. [38]

    L. P . de Gioia and A.-M. Raclariu,Eikonal approximation in celestial CFT, JHEP 03, 030 (2023), doi:10.1007 /JHEP03(2023)030, 2206.10547

    2023 arXiv

  32. [39]

    Banerjee, R

    S. Banerjee, R. Mandal, A. Manu and P . Paul, MHV gluon scattering in the massive scalar background and celestial OPE, JHEP 10, 007 (2023), doi:10.1007 /JHEP10(2023)007, 2302.10245. 38 SciPost Physics Submission

    2023 arXiv

  33. [40]

    A. Ball, S. De, A. Yelleshpur Srikant and A. Volovich, Scalar-graviton amplitudes and celestial holography, JHEP 02, 097 (2024), doi:10.1007/JHEP02(2024)097, 2310.00520

    2024 arXiv

  34. [41]

    Crawley , A

    E. Crawley , A. Guevara, E. Himwich and A. Strominger, Self-dual black holes in celestial holography, JHEP 09, 109 (2023), doi:10.1007/JHEP09(2023)109, 2302.06661

    2023 arXiv

  35. [42]

    Banerjee, S

    S. Banerjee, S. Ghosh, P . Pandey and A. P . Saha, Modified celestial amplitude in Einstein gravity, JHEP 03, 125 (2020), doi:10.1007/JHEP03(2020)125, 1909.03075

    2020 arXiv

  36. [43]

    Adamo, W

    T . Adamo, W . Bu, P . Tourkine and B. Zhu,Eikonal amplitudes on the celestial sphere, JHEP 10, 192 (2024), doi:10.1007 /JHEP10(2024)192, 2405.15594

    2024 arXiv

  37. [44]

    Adamo, A

    T . Adamo, A. Cristofoli and P . Tourkine,Eikonal amplitudes from curved backgrounds, SciPost Phys. 13(2), 032 (2022), doi:10.21468 /SciPostPhys.13.2.032, 2112.09113

    2022 arXiv

  38. [45]

    Amati, M

    D. Amati, M. Ciafaloni and G. Veneziano, Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions, Int. J. Mod. Phys. A 3, 1615 (1988), doi:10.1142 /S0217751X88000710

    1988

  39. [46]

    D. N. Kabat and M. Ortiz, Eikonal quantum gravity and Planckian scattering, Nucl. Phys. B 388, 570 (1992), doi:10.1016 /0550-3213(92)90627-N, hep-th/9203082

    1992 arXiv

  40. [47]

    H. W . Hamber,Quantum gravitation: The Feynman path integral approach, Springer, Berlin, doi:10.1007 /978-3-540-85293-3 (2009)

    2009

  41. [48]

    Weyl, Space, Time, Matter, Dover, USA, doi:https://store.doverpublications.com/0486602672.html (1922)

    H. Weyl, Space, Time, Matter, Dover, USA, doi:https://store.doverpublications.com/0486602672.html (1922)

    1922

  42. [49]

    Utiyama and B

    R. Utiyama and B. S. DeWitt, Renormalization of a Classical Gravitational Field Interacting with Quantized Matter Fields, Journal of Mathematical Physics 3(4), 608 (1962), doi:10.1063 /1.1724264

    1962

  43. [50]

    K. S. Stelle, Renormalization of higher-derivative quantum gravity, Phys. Rev. D 16, 953 (1977), doi:10.1103 /PhysRevD.16.953

    1977

  44. [51]

    Pais and G

    A. Pais and G. E. Uhlenbeck, On field theories with non-localized action, Phys. Rev. 79, 145 (1950), doi:10.1103 /PhysRev.79.145

    1950

  45. [52]

    Fradkin and A

    E. Fradkin and A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nuclear Physics B 201(3), 469 (1982), doi:https://doi.org/10.1016/0550-3213(82)90444-8

    1982 doi

  46. [53]

    Y. Abe, T . Inami, K. Izumi and T . Kitamura, Matter scattering in quadratic gravity and unitarity, PTEP 2018(3), 031E01 (2018), doi:10.1093/ptep/pty010, 1712.06305

    2018 arXiv

  47. [54]

    Y. Abe, T . Inami, K. Izumi, T . Kitamura and T . Noumi, S-matrix Unitarity and Renormalizability in Higher Derivative Theories, PTEP 2019(8), 083B06 (2019), doi:10.1093 /ptep/ptz084, 1805.00262

    2019 arXiv

  48. [55]

    Y. Abe, T . Inami and K. Izumi,Perturbative S-matrix unitarity (S†S = 1) in R2 µν gravity, Mod. Phys. Lett. A 36(16), 2150105 (2021), doi:10.1142 /S0217732321501054, 2012.01717. 39 SciPost Physics Submission

    2021 arXiv

  49. [56]

    Y. Abe, T . Inami and K. Izumi, High-energy properties of the graviton scattering in quadratic gravity, JHEP 03, 213 (2023), doi:10.1007 /JHEP03(2023)213, 2210.13666

    2023 arXiv

  50. [57]

    Llewellyn Smith, High energy behaviour and gauge symmetry, Physics Letters B 46(2), 233 (1973), doi:https: //doi.org/10.1016/0370-2693(73)90692-8

    C. Llewellyn Smith, High energy behaviour and gauge symmetry, Physics Letters B 46(2), 233 (1973), doi:https: //doi.org/10.1016/0370-2693(73)90692-8

    1973 doi

  51. [58]

    Lévy and J

    M. Lévy and J. Sucher, Eikonal approximation in quantum field theory, Phys. Rev. 186, 1656 (1969), doi:10.1103 /PhysRev.186.1656

    1969

  52. [60]

    ’t Hooft, Graviton Dominance in Ultrahigh-Energy Scattering, Phys

    G. ’t Hooft, Graviton Dominance in Ultrahigh-Energy Scattering, Phys. Lett. B 198, 61 (1987), doi:10.1016 /0370-2693(87)90159-6

    1987

  53. [61]

    M. A. Maroun, Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory, Ph.D. thesis, UC Riverside, ProQuest ID: Maroun_ucr_0032D_11407, Merritt ID: ark:/13030/m5s46ws7 (2013)

    2013

  54. [62]

    G. W . Johnson and M. L. Lapidus,The Feynman Integral and Feynman’s Operational Calculus, Oxford University Press, New York (2000)

    2000

  55. [63]

    Borji and Y

    M. Borji and Y. Pano, Distributional celestial amplitudes, JHEP 07, 120 (2024), doi:10.1007/JHEP07(2024)120, 2401.08877

    2024 arXiv

  56. [64]

    Beneke and V

    M. Beneke and V . A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522, 321 (1998), doi:10.1016 /S0550-3213(98)00138-2, hep-ph/9711391

    1998 arXiv

  57. [65]

    F . A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678, 491 (2004), doi:10.1016 /j.nuclphysb.2003.11.016, hep-th/0309180

    2004 arXiv

  58. [66]

    Mukhametzhanov and A

    B. Mukhametzhanov and A. Zhiboedov, Analytic Euclidean Bootstrap, JHEP 10, 270 (2019), doi:10.1007 /JHEP10(2019)270, 1808.03212

    2019 arXiv

  59. [67]

    Fan, Celestial conformal blocks of massless scalars and analytic continuation of the Appell function F1, JHEP 01, 145 (2024), doi:10.1007 /JHEP01(2024)145, 2311.11345

    W . Fan, Celestial conformal blocks of massless scalars and analytic continuation of the Appell function F1, JHEP 01, 145 (2024), doi:10.1007 /JHEP01(2024)145, 2311.11345

    2024 arXiv

  60. [68]

    J. L. Burchnall and T . W . Chaundy ,Expansions of appell’s double hypergeometric functions, Quarterly Journal of Mathematics 1, 249 (1940)

    1940

  61. [69]

    M. S. Costa, V . Goncalves and J. Penedones,Conformal Regge theory, JHEP 12, 091 (2012), doi:10.1007 /JHEP12(2012)091, 1209.4355

    2012 arXiv

  62. [70]

    J. Liu, D. Meltzer, D. Poland and D. Simmons-Duffin, The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT, JHEP 09, 115 (2020), doi:10.1007 /JHEP09(2020)115, [Erratum: JHEP 01, 206 (2021)], 2007.07914

    2020 arXiv

  63. [71]

    L. U. Ancarani and G. Gasaneo, Derivatives of any order of the Gaussian hypergeometric function (2)F1(a, b, c z) with respect to the parameters a, b and c, J. Phys. A 42, 395208 (2009), doi:10.1088 /1751-8113/42/39/395208. 40 SciPost Physics Submission

    2009

  64. [72]

    Donnay , A

    L. Donnay , A. Fiorucci, Y. Herfray and R. Ruzziconi, Carrollian Perspective on Celestial Holography, Phys. Rev. Lett. 129(7), 071602 (2022), doi:10.1103 /PhysRevLett.129.071602, 2202.04702

    2022 arXiv

  65. [73]

    Donnay , A

    L. Donnay , A. Fiorucci, Y. Herfray and R. Ruzziconi, Bridging Carrollian and celestial holography, Phys. Rev. D 107(12), 126027 (2023), doi:10.1103/PhysRevD.107.126027, 2212.12553

    2023 arXiv

  66. [74]

    Bagchi, S

    A. Bagchi, S. Banerjee, R. Basu and S. Dutta, Scattering Amplitudes: Celestial and Carrollian, Phys. Rev. Lett. 128(24), 241601 (2022), doi:10.1103 /PhysRevLett.128.241601, 2202.08438

    2022 arXiv

  67. [75]

    Pate, A.-M

    M. Pate, A.-M. Raclariu and A. Strominger, Gravitational Memory in Higher Dimensions, JHEP 06, 138 (2018), doi:10.1007/JHEP06(2018)138, 1712.01204

    2018 arXiv

  68. [76]

    Banerjee, R

    S. Banerjee, R. Basu and S. Atul Bhatkar, Light transformed gluon correlators in CCFT, JHEP 01, 075 (2023), doi:10.1007 /JHEP01(2023)075, 2203.06657

    2023 arXiv

  69. [77]

    S. A. Narayanan, Marginality from Leading Soft Gluons (2024), 2407.12521

    2024 arXiv

  70. [78]

    Banerjee, R

    S. Banerjee, R. Basu and S. Atul Bhatkar, Light transformation: a celestial and Carrollian perspective, JHEP 12, 122 (2024), doi:10.1007/JHEP12(2024)122, 2407.08379. 41

    2024 arXiv

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