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REVIEW 2 major objections 4 minor 7 cited by

Existing loop-level soft-gluon data force the celestial OPE of mixed-helicity currents to carry energy-fraction coefficients, which breaks holomorphic factorization and makes double collinear limits non-associative.

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2026-08-03 13:52 UTC pith:6D4LD2K6

load-bearing objection A careful translation of known QCD soft-current data into celestial language; the main new claims are real, but the "never ambiguous" headline depends on a soft-first ordering that the abstract should state explicitly. the 2 major comments →

arxiv 2512.22104 v2 pith:6D4LD2K6 submitted 2025-12-26 hep-th hep-ph

Non-abelian soft radiation data for a celestial theory

Lorenzo Magnea , Enrico Zunino This is my paper
classification hep-th hep-ph
keywords celestial holographysoft gluon currentsoperator product expansionnon-abelian gauge theorycollinear limitsassociativityrunning couplingeikonal factorization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that decades of perturbative data on soft gluon emission, translated to the celestial sphere, strongly constrain any proposed celestial conformal field theory (CFT). The single soft current's loop logarithms can all be reabsorbed into the running of the d-dimensional coupling evaluated at dipole transverse momenta, so a logarithmic celestial CFT may be unnecessary. The double and triple soft currents, in collinear limits, impose celestial operator product expansions that are never ambiguous but carry coefficients depending on gluon energy fractions; these coefficients break holomorphic factorization and, for mixed helicities, break associativity of successive limits. The paper concludes that the soft sector of a non-abelian gauge theory is not captured by a standard local two-dimensional conformal field theory, though it remains surprisingly close to an OPE structure.

Core claim

The central discovery, on the paper's own terms, is that the celestial OPEs suggested by multiple-emission currents are unambiguous because the continuous parameter governing the interpolation between strongly-ordered limits is the gluon energy fraction. For opposite-helicity gluons the OPE of a holomorphic current with an antiholomorphic current is nonvanishing, with weights given by energy fractions, which rules out holomorphic factorization. Taking two collinear limits in different orders on the triple soft current yields different energy-fraction factors, so associativity fails; strongly-ordered limits restore associativity but reintroduce the known ambiguity. In parallel, all logarithms

What carries the argument

The load-bearing objects are the multiple soft-gluon emission currents (eikonal form factors) written in celestial coordinates. Their collinear limits define celestial current OPEs, and the double and triple currents supply the data needed to test associativity. The key identity is the mixed-helicity OPE j(z) jbar(w) ~ [y/(z-w)] jbar + [(1-y)/(bar z - bar w)] j, with y an energy fraction, which simultaneously removes the earlier strong-ordering ambiguity and produces non-associativity. For the single current, the key mechanism is re-expressing eikonal scale factors as the d-dimensional running coupling evaluated at each dipole's transverse momentum, reabsorbing all logarithms.

Load-bearing premise

The paper's central conclusion depends on always taking the soft limit before the collinear limit; if one instead takes collinear limits of hard amplitudes first and then performs a Mellin transform, the two orders of limits do not commute, and the energy-fraction-dependent, non-associative OPE might be an artifact of the chosen ordering.

What would settle it

Compute the double and triple collinear limits of the same soft currents using the standard splitting-function route (hard collinear limit first, then Mellin transform to the celestial basis) with identical kinematics. If the resulting OPE coefficients are independent of energy fractions or do not reproduce the paper's energy-fraction OPE and its order-dependence, then the paper's central claim would be an artifact of the soft-first ordering and would fail.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The mixed-helicity celestial OPE is fixed by bulk data, not ambiguous, so attempts to define the OPE by choosing a strong ordering are superseded by a continuous energy-fraction interpolation.
  • Any celestial theory with holomorphic factorization, such as a free-boson or otherwise factorizable theory, is excluded at the level of soft currents.
  • The soft current OPE is not associative when helicities mix: successive collinear limits of triple emission give different results depending on order, so the naive product of soft insertions cannot be represented by local operators on the sphere.
  • The single soft current's loop logarithms are reabsorbed into the running coupling, so a logarithmic celestial CFT is not required by this data; scale dependence enters as external bulk information.
  • In strongly-ordered limits, the one-loop OPE requires all lower-order single soft currents, so the simple current-algebra picture does not extend beyond tree level.

Where Pith is reading between the lines

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

  • If the energy-fraction OPE is genuine, the celestial theory likely needs non-local or smeared degrees of freedom, such as continuous color and energy distributions, rather than point operators; the paper gestures at this but does not assert it.
  • The soft-first versus collinear-first order of limits is the main loophole: a derivation of the celestial OPE from hard splitting functions followed by a Mellin transform might produce different coefficients, and a direct comparison would confirm or refute the paper's central claim.
  • The same energy-fraction mechanism should appear in gravity and in supersymmetric extensions, since collinear splitting weights are universal; computing mixed-helicity double or triple graviton soft currents would test whether non-associativity is generic.
  • The dipole-scale running-coupling reorganization suggests a practical resummation scheme for soft currents: evaluating the coupling at each dipole's transverse momentum should systematically eliminate UV logarithms at higher loops, which is testable once the three-loop multi-leg soft current is available.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper collects known perturbative QCD results for single, double, and triple soft-gluon emission currents, translates them into celestial-sphere coordinates, and extracts consequences for a putative celestial conformal field theory (CCFT). The main claims are: (i) all logarithms appearing in the loop expansion of the single soft current can be reabsorbed into the scale dependence of the d-dimensional running coupling, so that a logarithmic celestial CFT may be unnecessary; (ii) collinear limits of the uniform multiple-soft-emission currents yield OPE-like structures that are ``never ambiguous'' but involve energy-fraction-dependent coefficients, breaking holomorphic factorization; and (iii) in double collinear limits these structures fail associativity for mixed-helicity currents, while strongly-ordered limits restore associativity at the price of reintroducing the known ordering ambiguity. The analysis is explicitly performed in a ``soft limit first, collinear limit second'' convention, which the paper itself notes does not commute with the standard celestial-OPE route.

Significance. If the claims hold, the paper provides a sharp, data-driven constraint on celestial holography: the soft sector of non-abelian gauge theory cannot be described by a standard local 2D CFT with holomorphic factorization, and the energy-fraction weights in the OPE coefficients single out a specific interpolation between previously ambiguous strongly-ordered limits. The paper is valuable as a systematic compendium of known high-order QCD soft-current data translated into celestial coordinates, with detailed and explicit expressions (e.g., Eqs. (4.3), (4.14), (4.24), (5.3)-(5.5), (5.7), (5.12), (6.5)-(6.14)). The derivations are direct translations of independently computed gauge-theory amplitudes; no fitting parameters are introduced. The main weakness is that the headline ``never ambiguous'' claim is tied to the soft-first ordering, while the paper itself acknowledges that this ordering does not commute with the standard celestial-OPE definition.

major comments (2)
  1. [Abstract; §5; §7] The central claim that the celestial OPEs are ``never ambiguous'' is stated in the abstract without the qualification that this holds in the soft-first convention adopted in §5. The paper explicitly says there that ``the two order of limits in general do not commute'' and that the standard route is collinear limit of hard amplitudes followed by Mellin transform and then the conformally soft limit. The coefficients in Eqs. (5.7), (5.12), (6.13) and (6.14) depend on energy fractions x12 and yi; a Mellin transform over the soft energies could integrate these into conformal-weight-dependent coefficients, so the two routes need not give the same OPE. Please either restrict the ``never ambiguous'' statement to the soft-first framework throughout, or compare explicitly with the standard route and show that the OPE coefficients are unchanged. This is load-bearing for the paper's main conclusion.
  2. [§4.2, Eqs. (4.21)-(4.25)] The all-orders statement that ``all logarithms'' in the single soft current are reabsorbed by the running d-dimensional coupling is supported by explicit two-loop checks and by a dimensional/scaling argument, but it is not demonstrated to all orders. In particular, the argument selects dipole transverse-momentum scales qij^2, but higher-multipole contributions involve more complex kinematic functions (e.g., F(z_iqjk, ε) in Eq. (4.16)), and it is not shown that a simultaneous scale redefinition absorbs every logarithm while preserving the color structure. Since the abstract presents this as a result, please either prove the all-orders claim or clearly label it as an extrapolation/conjecture supported by known low-order data.
minor comments (4)
  1. [Throughout] Several typos and misspellings: ``Minkowsky'' in §1, ``sistematically'' in §5, ``tipical'' in §4.1, ``chellenges'' in §1, ``cooordinates'' in §7. Please proofread.
  2. [§6, after Eq. (6.2)] The associativity analysis is restricted to the maximally non-abelian term Γ in Eq. (6.1). The statement that the first two lines are ``not relevant'' for triple collinear singularities is plausible but is not shown explicitly. A sentence explaining why the abelian-like and two-gluon-attachment terms are subleading in the successive collinear limits would make the check of associativity more airtight.
  3. [§5.1, Eq. (5.12)] The notation ``u1'' and ``u2'' for celestial coordinates is introduced in Eq. (5.10) but then the OPE in Eq. (5.12) mixes u and z variables. Please harmonize the notation so that the celestial coordinates of the soft gluons are denoted consistently.
  4. [§2, Eq. (2.11)] In Eq. (2.11), the prefactor K(αs(μ), ε) is written with the scale μ but the text sometimes uses μ^2; please ensure consistent arguments for αs and the logarithm.

Circularity Check

0 steps flagged

No significant circularity: the OPE claims are read off from independent published gauge-theory amplitudes, and the RG reabsorption is a scale reparametrization, not a fitted prediction.

full rationale

The paper's derivation chain is self-contained with respect to the host of independent perturbative QCD results it uses. The central OPE claims in Sections 5 and 6 are obtained by writing the known tree-level double and triple soft currents (Eqs. (5.1), (6.1), from Catani–Grazzini and Catani–Colferai–Torrini, none of which are by the authors) in celestial coordinates and then taking collinear limits (Eqs. (5.6)–(5.7), (5.11)–(5.12), (6.11)–(6.14)). The energy-fraction coefficients and the non-associativity are read off from these explicit amplitude expressions, not fitted or imposed; no parameter is adjusted to reproduce the claimed result. The reabsorption of logarithms in Section 4 is also not circular: it uses the standard solution of the d-dimensional RG equation (Eqs. (4.11)–(4.12), (4.21)–(4.24)) to change the scale of the running coupling, and it is checked against the explicit one- and two-loop soft-current results. This is a reparametrization of known expressions rather than a derivation of a target from itself. The self-citations present ([14], [41], [42]) provide context, the free-boson correspondence, and strongly-ordered factorization theorems, but the load-bearing OPE analysis does not reduce to those citations; it is independently verified against Refs. [22,23,24,44,71,78]. Finally, the soft-first ordering is a declared convention, and the paper explicitly acknowledges that the two orders of limits do not commute. That is a scope/correctness caveat, not a circular reduction. Hence no circular step is identified.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The paper introduces no new free parameters or invented entities. Its conclusions rely on standard leading-power factorization, the celestial-coordinate dictionary, the specific order of limits (soft before collinear), and the correctness of previously published soft-current expressions. The reabsorption of logarithms uses the ordinary RG running of the strong coupling without fitting any constants.

axioms (5)
  • domain assumption Leading-power soft factorization of scattering amplitudes holds to all orders (Eq. (3.4), Section 3).
    The entire celestial interpretation rests on the soft current factorizing the amplitude at leading power; the paper treats this as established for all m and n.
  • domain assumption The standard celestial-sphere parametrization of null momenta and polarizations (Eqs. (3.8)–(3.13)).
    Used throughout to translate momentum-space currents into celestial coordinates.
  • ad hoc to paper The soft limit is taken before the collinear limit when defining celestial OPEs (Section 5).
    The paper explicitly adopts this order of limits, and acknowledges the two orders do not commute; the OPE conclusions depend on this choice.
  • standard math The d-dimensional running coupling obeys the RG equation (2.3) and α_s(μ^2)(μ^2/q^2)^ε = α_s(q^2,ε) at leading order.
    This is standard QCD RG analysis, used to reabsorb logarithms in the single-soft current.
  • domain assumption The cited gauge-theory results for soft currents (Refs. [20,21,22,23,24,44]) are correct at the stated orders.
    The paper re-expresses these known results; any error in the original computations would propagate, but these are established results in the QCD literature.

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0 comments
read the original abstract

Celestial holography posits that the long-distance behavior of gauge and gravity theories is dictated by two-dimensional conformal field theories defined on the celestial sphere. For non-abelian gauge theories, this proposal is verified, to all perturbative orders, by dipole color correlations in the infrared factor of non-abelian scattering amplitudes, which are given by a correlator of matrix-valued vertex operators in a free-boson theory on the sphere. Decades of high-order gauge-theory calculations have provided a number of further results that can be used to test and constrain a possible celestial theory: they include explicit expressions for soft emission currents up to three particles, and up to three loops for single soft emission. In this paper, we analyze this trove of data, appropriately translated in the celestial language, and we use them to extract information on the celestial theory. In particular, we show that all logarithms arising in the loop expansion of the single soft current can be reabsorbed in the scale choices for the $d$-dimensional coupling, casting some doubt on the need for a logarithmic celestial theory. We then note that the celestial OPEs suggested by the structure of multiple emission currents in collinear limits are never ambiguous, but involve coefficients depending on gluon energy fractions, which break holomorphic factorization, as well as associativity when double limits are taken. Strongly-ordered soft limits recover associativity, but suffer from ambiguities already discussed in earlier literature.

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Reference graph

Works this paper leans on

87 extracted references · 74 linked inside Pith · cited by 5 Pith papers

  1. [1]

    Bloch and A

    F. Bloch and A. Nordsieck,Note on the Radiation Field of the electron,Phys. Rev.52(1937) 54

    1937

  2. [2]

    Agarwal, L

    N. Agarwal, L. Magnea, C. Signorile-Signorile and A. Tripathi,The infrared structure of perturbative gauge theories,Phys. Rept.994(2023) 1 [2112.07099]

    Pith/arXiv arXiv 2023

  3. [3]

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

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

    Pith/arXiv arXiv 2014

  4. [4]

    Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory,1703.05448

    A. Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory,1703.05448

    Pith/arXiv arXiv

  5. [5]

    Arkani-Hamed, M

    N. Arkani-Hamed, M. Pate, A.-M. Raclariu and A. Strominger,Celestial Amplitudes from UV to IR, 2012.04208

    Pith/arXiv arXiv 2012

  6. [6]

    Pasterski, S.-H

    S. Pasterski, S.-H. Shao and A. Strominger,Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere,Phys. Rev. D96(2017) 065026 [1701.00049]

    Pith/arXiv arXiv 2017

  7. [7]

    Pasterski and S.-H

    S. Pasterski and S.-H. Shao,Conformal basis for flat space amplitudes,Phys. Rev. D96(2017) 065022 [1705.01027]

    Pith/arXiv arXiv 2017

  8. [8]

    Pasterski, M

    S. Pasterski, M. Pate and A.-M. Raclariu,Celestial Holography, inSnowmass 2021, 11, 2021 [2111.11392]

    Pith/arXiv arXiv 2021

  9. [9]

    Pasterski,A Chapter on Celestial Holography,2310.04932

    S. Pasterski,A Chapter on Celestial Holography,2310.04932

    Pith/arXiv arXiv

  10. [10]

    W. Fan, A. Fotopoulos and T.R. Taylor,Soft Limits of Yang-Mills Amplitudes and Conformal Correlators,JHEP05(2019) 121 [1903.01676]

    Pith/arXiv arXiv 2019

  11. [11]

    Pasterski, S.-H

    S. Pasterski, S.-H. Shao and A. Strominger,Gluon Amplitudes as 2d Conformal Correlators,Phys. Rev. D96(2017) 085006 [1706.03917]

    Pith/arXiv arXiv 2017

  12. [12]

    Schreiber, A

    A. Schreiber, A. Volovich and M. Zlotnikov,Tree-level gluon amplitudes on the celestial sphere,Phys. Lett. B781(2018) 349 [1711.08435]

    Pith/arXiv arXiv 2018

  13. [13]

    Gonz´ alez, A

    H.A. Gonz´ alez, A. Puhm and F. Rojas,Loop corrections to celestial amplitudes,Phys. Rev. D102 (2020) 126027 [2009.07290]

    Pith/arXiv arXiv 2020

  14. [14]

    Magnea,Non-abelian infrared divergences on the celestial sphere,JHEP05(2021) 282 [2104.10254]

    L. Magnea,Non-abelian infrared divergences on the celestial sphere,JHEP05(2021) 282 [2104.10254]. – 28 –

    Pith/arXiv arXiv 2021

  15. [15]

    Gonz´ alez and F

    H.A. Gonz´ alez and F. Rojas,The structure of IR divergences in celestial gluon amplitudes,JHEP 2021(2021) 171 [2104.12979]

    Pith/arXiv arXiv 2021

  16. [16]

    Almelid, C

    O. Almelid, C. Duhr and E. Gardi,Three-loop corrections to the soft anomalous dimension in multileg scattering,Phys. Rev. Lett.117(2016) 172002 [1507.00047]

    Pith/arXiv arXiv 2016

  17. [17]

    Almelid, C

    O. Almelid, C. Duhr, E. Gardi, A. McLeod and C.D. White,Bootstrapping the QCD soft anomalous dimension,JHEP09(2017) 073 [1706.10162]

    Pith/arXiv arXiv 2017

  18. [18]

    Gardi and L

    E. Gardi and L. Magnea,Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes,JHEP0903(2009) 079 [0901.1091]

    Pith/arXiv arXiv 2009

  19. [19]

    Becher and M

    T. Becher and M. Neubert,Infrared singularities of scattering amplitudes and N 3LL resummation for n-jet processes,JHEP01(2020) 025 [1908.11379]

    Pith/arXiv arXiv 2020

  20. [20]

    Dixon, E

    L.J. Dixon, E. Herrmann, K. Yan and H.X. Zhu,Soft gluon emission at two loops in full color,JHEP 05(2020) 135 [1912.09370]

    Pith/arXiv arXiv 2020

  21. [21]

    Herzog, Y

    F. Herzog, Y. Ma, B. Mistlberger and A. Suresh,Single-soft emissions for amplitudes with two colored particles at three loops,JHEP12(2023) 023 [2309.07884]

    Pith/arXiv arXiv 2023

  22. [22]

    Zhu,Double soft current at one-loop in QCD,2009.08919

    Y.J. Zhu,Double soft current at one-loop in QCD,2009.08919

    arXiv 2009

  23. [23]

    Czakon, F

    M. Czakon, F. Eschment and T. Schellenberger,Revisiting the double-soft asymptotics of one-loop amplitudes in massless QCD,JHEP04(2023) 065 [2211.06465]

    Pith/arXiv arXiv 2023

  24. [24]

    Catani, D

    S. Catani, D. Colferai and A. Torrini,Triple (and quadruple) soft-gluon radiation in QCD hard scattering,JHEP01(2020) 118 [1908.01616]

    Pith/arXiv arXiv 2020

  25. [25]

    Sen,Asymptotic Behavior of the Wide Angle On-Shell Quark Scattering Amplitudes in Nonabelian Gauge Theories,Phys

    A. Sen,Asymptotic Behavior of the Wide Angle On-Shell Quark Scattering Amplitudes in Nonabelian Gauge Theories,Phys. Rev.D28(1983) 860

    1983

  26. [26]

    Botts and G.F

    J. Botts and G.F. Sterman,Hard Elastic Scattering in QCD: Leading Behavior,Nucl. Phys. B325 (1989) 62

    1989

  27. [27]

    Dixon, L

    L.J. Dixon, L. Magnea and G. Sterman,Universal structure of subleading infrared poles in gauge theory amplitudes,JHEP08(2008) 022 [0805.3515]

    Pith/arXiv arXiv 2008

  28. [28]

    Feige and M.D

    I. Feige and M.D. Schwartz,Hard-Soft-Collinear Factorization to All Orders,Phys. Rev.D90(2014) 105020 [1403.6472]

    Pith/arXiv arXiv 2014

  29. [29]

    Bassetto, M

    A. Bassetto, M. Ciafaloni and G. Marchesini,Jet Structure and Infrared Sensitive Quantities in Perturbative QCD,Phys. Rept.100(1983) 201

    1983

  30. [30]

    Catani and M.H

    S. Catani and M.H. Seymour,A general algorithm for calculating jet cross sections in NLO QCD, Nucl. Phys.B485(1997) 291 [hep-ph/9605323]

    Pith/arXiv arXiv 1997

  31. [31]

    Becher and M

    T. Becher and M. Neubert,Infrared singularities of scattering amplitudes in perturbative QCD,Phys. Rev. Lett.102(2009) 162001 [0901.0722]

    Pith/arXiv arXiv 2009

  32. [32]

    Becher and M

    T. Becher and M. Neubert,On the Structure of Infrared Singularities of Gauge-Theory Amplitudes, JHEP06(2009) 081 [0903.1126]

    Pith/arXiv arXiv 2009

  33. [33]

    Gardi and L

    E. Gardi and L. Magnea,Infrared singularities in QCD amplitudes,Nuovo Cim.032C(2009) 137 [0908.3273]

    Pith/arXiv arXiv 2009

  34. [34]

    von Manteuffel, E

    A. von Manteuffel, E. Panzer and R.M. Schabinger,Analytic four-loop anomalous dimensions in massless QCD from form factors,2002.04617

    Pith/arXiv arXiv 2002

  35. [35]

    Brown,Polylogarithmes multiples uniformes en une variable,Compt

    F.C.S. Brown,Polylogarithmes multiples uniformes en une variable,Compt. Rend. Math.338(2004) 527

    2004

  36. [36]

    Catani, B.R

    S. Catani, B.R. Webber and G. Marchesini,QCD coherent branching and semiinclusive processes at large x,Nucl. Phys. B349(1991) 635. – 29 –

    1991

  37. [37]

    Grozin, J.M

    A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard,The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions,JHEP01(2016) 140 [1510.07803]

    Pith/arXiv arXiv 2016

  38. [38]

    Catani, D

    S. Catani, D. De Florian and M. Grazzini,Soft-gluon effective coupling and cusp anomalous dimension,Eur. Phys. J. C79(2019) 685 [1904.10365]

    Pith/arXiv arXiv 2019

  39. [39]

    Kinoshita,Mass singularities of Feynman amplitudes,J

    T. Kinoshita,Mass singularities of Feynman amplitudes,J. Math. Phys.3(1962) 650

    1962

  40. [40]

    Lee and M

    T.D. Lee and M. Nauenberg,Degenerate Systems and Mass Singularities,Phys. Rev.133(1964) B1549

    1964

  41. [41]

    Magnea, E

    L. Magnea, E. Maina, G. Pelliccioli, C. Signorile-Signorile, P. Torrielli and S. Uccirati,Factorisation and Subtraction beyond NLO,JHEP12(2018) 062 [1809.05444]

    Pith/arXiv arXiv 2018

  42. [42]

    Magnea, C

    L. Magnea, C. Milloy, C. Signorile-Signorile and P. Torrielli,Strongly-ordered infrared counterterms from factorisation,JHEP06(2024) 021 [2403.11975]

    Pith/arXiv arXiv 2024

  43. [43]

    Catani,The Singular behavior of QCD amplitudes at two loop order,Phys.Lett.B427(1998) 161 [hep-ph/9802439]

    S. Catani,The Singular behavior of QCD amplitudes at two loop order,Phys.Lett.B427(1998) 161 [hep-ph/9802439]

    Pith/arXiv arXiv 1998

  44. [44]

    Catani and M

    S. Catani and M. Grazzini,Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond,Nucl. Phys. B570(2000) 287 [hep-ph/9908523]

    Pith/arXiv arXiv 2000

  45. [45]

    Pate, A.-M

    M. Pate, A.-M. Raclariu and A. Strominger,Conformally Soft Theorem in Gauge Theory,Phys. Rev. D100(2019) 085017 [1904.10831]

    Pith/arXiv arXiv 2019

  46. [46]

    Pasterski,Lectures on celestial amplitudes,Eur

    S. Pasterski,Lectures on celestial amplitudes,Eur. Phys. J. C81(2021) 1062 [2108.04801]

    Pith/arXiv arXiv 2021

  47. [47]

    Y. Ma, G. Sterman and A. Venkata,Soft Photon Theorem in QCD with Massless Quarks,Phys. Rev. Lett.132(2024) 091902 [2311.06912]

    Pith/arXiv arXiv 2024

  48. [48]

    Z. Bern, V. Del Duca and C.R. Schmidt,The Infrared behavior of one loop gluon amplitudes at next-to-next-to-leading order,Phys. Lett. B445(1998) 168 [hep-ph/9810409]

    Pith/arXiv arXiv 1998

  49. [49]

    Z. Bern, V. Del Duca, W.B. Kilgore and C.R. Schmidt,The infrared behavior of one loop QCD amplitudes at next-to-next-to leading order,Phys. Rev. D60(1999) 116001 [hep-ph/9903516]

    Pith/arXiv arXiv 1999

  50. [50]

    Catani and M

    S. Catani and M. Grazzini,The soft gluon current at one loop order,Nucl. Phys. B591(2000) 435 [hep-ph/0007142]

    Pith/arXiv arXiv 2000

  51. [51]

    Bhardwaj and A

    R. Bhardwaj and A. Yelleshpur Srikant,Celestial soft currents at one-loop and their OPEs,JHEP 07(2024) 034 [2403.10443]

    Pith/arXiv arXiv 2024

  52. [52]

    Bissi, L

    A. Bissi, L. Donnay and B. Valsesia,Logarithmic doublets in CCFT,JHEP12(2024) 031 [2407.17123]

    Pith/arXiv arXiv 2024

  53. [53]

    Fiorucci, D

    A. Fiorucci, D. Grumiller and R. Ruzziconi,Logarithmic celestial conformal field theory,Phys. Rev. D109(2024) L021902 [2305.08913]

    Pith/arXiv arXiv 2024

  54. [54]

    Kogan and A

    I.I. Kogan and A. Lewis,Origin of logarithmic operators in conformal field theories,Nucl. Phys. B 509(1998) 687 [hep-th/9705240]

    Pith/arXiv arXiv 1998

  55. [55]

    Flohr,Bits and pieces in logarithmic conformal field theory,Int

    M. Flohr,Bits and pieces in logarithmic conformal field theory,Int. J. Mod. Phys. A18(2003) 4497 [hep-th/0111228]

    Pith/arXiv arXiv 2003

  56. [56]

    Creutzig and D

    T. Creutzig and D. Ridout,Logarithmic Conformal Field Theory: Beyond an Introduction,J. Phys. A46(2013) 4006 [1303.0847]

    Pith/arXiv arXiv 2013

  57. [57]

    Himwich, M

    E. Himwich, M. Pate and K. Singh,Celestial operator product expansions and w 1+∞ symmetry for all spins,JHEP01(2022) 080 [2108.07763]

    Pith/arXiv arXiv 2022

  58. [58]

    Guevara, E

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

    Pith/arXiv arXiv 2021

  59. [59]

    Magnea and G.F

    L. Magnea and G.F. Sterman,Analytic continuation of the Sudakov form-factor in QCD,Phys. Rev. D42(1990) 4222. – 30 –

    1990

  60. [60]

    Magnea,Analytic resummation for the quark form-factor in QCD,Nucl.Phys.B593(2001) 269 [hep-ph/0006255]

    L. Magnea,Analytic resummation for the quark form-factor in QCD,Nucl.Phys.B593(2001) 269 [hep-ph/0006255]

    Pith/arXiv arXiv 2001

  61. [61]

    Brown,Multiple zeta values and periods of moduli spaces M 0 ,n ( R ),Annales Sci

    F.C.S. Brown,Multiple zeta values and periods of moduli spaces M 0 ,n ( R ),Annales Sci. Ecole Norm. Sup.42(2009) 371 [math/0606419]

    Pith/arXiv arXiv 2009

  62. [62]

    Remiddi and J

    E. Remiddi and J. Vermaseren,Harmonic polylogarithms,Int.J.Mod.Phys.A15(2000) 725 [hep-ph/9905237]

    Pith/arXiv arXiv 2000

  63. [63]

    Volovich, C

    A. Volovich, C. Wen and M. Zlotnikov,Double Soft Theorems in Gauge and String Theories,JHEP 07(2015) 095 [1504.05559]

    Pith/arXiv arXiv 2015

  64. [64]

    Klose, T

    T. Klose, T. McLoughlin, D. Nandan, J. Plefka and G. Travaglini,Double-Soft Limits of Gluons and Gravitons,JHEP07(2015) 135 [1504.05558]

    Pith/arXiv arXiv 2015

  65. [65]

    Pate, A.-M

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

    Pith/arXiv arXiv 2021

  66. [66]

    Mangano and S.J

    M.L. Mangano and S.J. Parke,Multiparton Amplitudes in Gauge Theories,Phys. Rept.200(1991) 301 [hep-th/0509223]

    Pith/arXiv arXiv 1991

  67. [67]

    Z. Bern, G. Chalmers, L.J. Dixon and D.A. Kosower,One loop N gluon amplitudes with maximal helicity violation via collinear limits,Phys. Rev. Lett.72(1994) 2134 [hep-ph/9312333]

    Pith/arXiv arXiv 1994

  68. [68]

    Bern, L.J

    Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower,One loop n point gauge theory amplitudes, unitarity and collinear limits,Nucl. Phys. B425(1994) 217 [hep-ph/9403226]

    Pith/arXiv arXiv 1994

  69. [69]

    Del Duca, C

    V. Del Duca, C. Duhr, E. Gardi, L. Magnea and C.D. White,An infrared approach to Reggeization, Phys.Rev.D85(2012) 071104 [1108.5947]

    Pith/arXiv arXiv 2012

  70. [70]

    Del Duca, C

    V. Del Duca, C. Duhr, E. Gardi, L. Magnea and C.D. White,The Infrared structure of gauge theory amplitudes in the high-energy limit,JHEP1112(2011) 021 [1109.3581]

    Pith/arXiv arXiv 2011

  71. [71]

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

    Pith/arXiv arXiv 2016

  72. [72]

    Bhardwaj, L

    R. Bhardwaj, L. Lippstreu, L. Ren, M. Spradlin, A. Yelleshpur Srikant and A. Volovich,Loop-level gluon OPEs in celestial holography,JHEP11(2022) 171 [2208.14416]

    Pith/arXiv arXiv 2022

  73. [73]

    Krishna,Celestial gluon and graviton OPE at loop level,JHEP03(2024) 176 [2310.16687]

    H. Krishna,Celestial gluon and graviton OPE at loop level,JHEP03(2024) 176 [2310.16687]

    Pith/arXiv arXiv 2024

  74. [74]

    Nastase, F

    H. Nastase, F. Rojas and C. Rubio,Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes,JHEP01(2022) 136 [2111.06861]

    Pith/arXiv arXiv 2022

  75. [75]

    Pranzetti and D.G

    D. Pranzetti and D.G. Salluce,Double-soft limit and celestial shadow OPE from charge bracket, 2510.26520

    arXiv

  76. [76]

    Freidel, D

    L. Freidel, D. Pranzetti and A.-M. Raclariu,Higher spin dynamics in gravity and w1+∞celestial symmetries,Phys. Rev. D106(2022) 086013 [2112.15573]

    Pith/arXiv arXiv 2022

  77. [77]

    Kapec,Soft particles and infinite-dimensional geometry,Class

    D. Kapec,Soft particles and infinite-dimensional geometry,Class. Quant. Grav.41(2024) 015001 [2210.00606]

    Pith/arXiv arXiv 2024

  78. [78]

    Ball,Celestial locality and the Jacobi identity,JHEP01(2023) 146 [2211.09151]

    A. Ball,Celestial locality and the Jacobi identity,JHEP01(2023) 146 [2211.09151]

    Pith/arXiv arXiv 2023

  79. [79]

    Kapec and P

    D. Kapec and P. Mitra,Shadows and soft exchange in celestial CFT,Phys. Rev. D105(2022) 026009 [2109.00073]

    Pith/arXiv arXiv 2022

  80. [80]

    Himwich and M

    E. Himwich and M. Pate,Shadow Celestial Operator Product Expansions,2505.09499

    Pith/arXiv arXiv

Showing first 80 references.