Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

UV considerations on scattering amplitudes in a web of theories

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Locality plus UV scaling fixes tree amplitudes across theories

desk verdict A solid extension of the on-shell bootstrap program with a genuinely new probe (single hard scaling); the proofs are clean where proven, but the acknowledged all-multiplicity gap is the main thing a referee should press on. read the letter →

arxiv 1908.08033 v2 pith:2UTERNGT submitted 2019-08-21 hep-th

John Joseph M. Carrasco , Laurentiu Rodina This is my paper · ORCID
classification hep-th
keywords scatteringamplitudesnonlinearsigmamodelBorn-InfeldspecialGalileondoublecopyBCFWshiftsinglehardscalingeffectivefieldtheory
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 argues that the tree-level scattering amplitudes of a family of effective field theories—the non-linear sigma model, bi-adjoint scalar, Born-Infeld, and special Galileon—are uniquely fixed by their high-energy (ultraviolet) scaling behavior once locality is assumed. To make this precise, the authors introduce a single-hard limit, sending one external momentum to infinity in a carefully chosen basis of kinematic invariants, and they determine the required scaling powers that select each theory. They prove that NLSM amplitudes follow from locality, unitarity, mass dimension two, and two UV scaling conditions, and they give evidence that unitarity can be dropped and instead emerge from locality plus UV constraints. Because these theories are linked by double-copy relations, the UV rules can be inherited from the building blocks, tying the constraints together across the web. If correct, the result puts effective field theories on the same on-shell footing as Yang-Mills and gravity, where IR and UV information each suffice to rebuild the amplitudes.

What carries the argument

The central object is the single hard scaling (SHS), a one-line deformation $p\to zp$ of a single external momentum, evaluated in a $p$-favoring basis of momentum invariants $\delta(i,[j,k])$ so that momentum conservation cannot obscure the growth in $z$. The growth rate $O(z^k)$ is enhanced, meaning smaller than naive power counting, only for special theories, and the compatibility of $\delta$ with the color or flavor ordering decides which scaling applies. The two-particle BCFW shift is the other UV probe, and the SHS is effectively half of it. These scalings carry the argument by forcing contact terms to vanish or to cancel against factorization channels, and the double-copy/KLT structure lets the scaling of composite theories such as Born-Infeld and the special Galileon be read off from the scalings of their factors, Yang-Mills and NLSM.

What would settle it

Compute the NLSM tree amplitude at eleven or twelve points, expand it in a $p$-favoring basis with a non-compatible $\delta$, and check whether the single-hard limit grows at most as $O(z^1)$; a single amplitude growing as $z^2$ would break Claim 3. Alternatively, run the same ansatz bootstrap at ten points and search for a local quartic object with mass dimension two, the claimed $O(z^0)/O(z^1)$ scalings, and unitarity that is not the NLSM amplitude.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that prescribed large-momentum scaling is a defining, not merely diagnostic, property of special amplitudes. Claim 3 states that NLSM amplitudes are uniquely fixed by locality, unitarity, and mass dimension two together with: single-hard scaling $A_n(\sigma)\sim O(z^0)$ when the chosen basis $\delta(i,[j,k])$ is compatible with the ordering $\sigma$, and $O(z^1)$ otherwise; and two-particle-shift scaling $O(z^1)$ for adjacent shifted legs and $O(z^0)$ for non-adjacent legs. The same logic fixes doubly-ordered bi-adjoint amplitudes from locality plus $O(z^{-3})/O(z^{-2})$ single-hard scaling, Born-Infeld from locality, unitarity, mass dimension $n$, and $O(z^0)$ BCFW scaling, and the special Galileon from locality, unitarity, and $O(z^3)$ single-hard scaling, with the last relying on an unproven uniqueness conjecture for the Galileon vertex. The paper further proves that NLSM amplitudes are fixed by locality, cyclic invariance, mass dimension two, and the BCJ color-kinematic relation, without assuming unitarity. Throughout, the authors present explicit checks that unitarity may be a consequence rather than an assumption: local ansätze subjected to UV scaling alone get fixed, with factorization emerging.

Load-bearing premise

The load-bearing premise is that the single-hard scaling laws imposed as constraints hold for every multiplicity; the paper verifies Yang-Mills through seven points and NLSM through ten points but has no all-multiplicity proof, and the special Galileon argument additionally depends on the unproven uniqueness of the Galileon vertex under its UV scalings.

Editorial extensions

If this is right

  • NLSM amplitudes need not be defined by the Adler zero; the same physics follows from locality plus two UV scaling conditions, so IR and UV descriptions become exchangeable.
  • If unitarity really emerges from locality and UV scaling, factorization is not an independent axiom for these theories, suggesting S-matrix formulations where locality and scaling are primary.
  • The double copy becomes a tool for predicting UV scaling: scaling powers of a composite theory are sums of the scaling powers of its factors, so constraints can be organized across the web rather than case by case.
  • Higher-derivative NLSM corrections are strongly constrained: with unitarity and BCJ relations, the $O(p^\kappa)$ contact terms are unique through $\kappa=10$ at six points, with the first ambiguity at $\kappa=12$.
  • The same single-hard-scaling bootstrap can likely be applied to other effective theories or supersymmetric variants; the paper already checks DBI-VA photon and fermion sectors through eight points.

Reading between the lines

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

  • If the scaling laws are proven at all multiplicities, the bootstrap becomes an algorithm: enumerate local ansätze, impose the single-hard scalings, and solve linear systems, with no Lagrangian needed.
  • Because the single-hard limit is half of a BCFW shift, two-particle-shift scaling can never be worse than single-hard scaling; this relation may be the seed of an inductive all-multiplicity proof for NLSM and Yang-Mills.
  • The apparent IR/UV equivalence for massless amplitudes hints that soft and hard limits are dual descriptions of the same on-shell data; probing this duality in celestial or Mellin-transformed amplitudes could be a fruitful test.
  • The unproven Galileon-vertex conjecture is the weakest link; extending the polynomial check beyond seven points, or proving the uniqueness via determinant identities, would complete the special-Galileon argument.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper investigates to what extent tree-level amplitudes in the 'web of theories' (Yang-Mills, gravity, bi-adjoint phi^3, NLSM, DBI-VA, Galileon and special Galileon) can be fixed by locality, unitarity, mass dimension, and UV scaling. The authors introduce a 'single hard scaling' (SHS) limit and use it alongside two-particle BCFW-type shifts. Section IV proves (Claim 1) that flavor-ordered NLSM amplitudes are uniquely determined by locality, mass dimension 2, cyclic invariance, and the BCJ relations, via reduction to the Adler zero. In Section V they claim that bi-adjoint amplitudes are fixed by locality and SHS (Claim 2, proven by induction in Appendix VIII.A); NLSM by locality, unitarity, and SHS/2S (Claim 3); sGal by locality, unitarity, mass dimension, SHS, and an unproven Conjecture 1 on the Galileon vertex (Claim 4); and BI by locality, unitarity, mass dimension, and two-particle shift scaling (Claim 5). They also provide low-multiplicity numerical and analytic checks suggesting that unitarity may be replaced by UV constraints.

Significance. If the proofs were complete, the paper would establish UV scaling as an on-shell principle as powerful as the IR Adler-zero soft bootstrap for a wide class of effective field theories, and would unify the double-copy web under a single UV constraint. The proof of Claim 1 is elegant and the explicit low-multiplicity checks (NLSM through 8/10 points, YM through 7, BI through 6, sGal through 6) are valuable evidence. The bi-adjoint induction in Appendix VIII.A is explicit and goes beyond mere verification. The double-copy argument in Sec. V.E gives a structural explanation for the SHS of composite theories, assuming the building-block scalings. However, the significance is currently conditional: the main uniqueness theorems rely on scaling laws whose all-multiplicity validity is unproven.

major comments (3)
  1. [Sec. III.E; Sec. V.A–V.D] The load-bearing assumption is that the SHS laws (66)–(74) and the 2S law (60)–(63) hold at arbitrary multiplicity. The text explicitly states that no all-multiplicity proof is available and that YM was checked through n=7 and NLSM through n=10 (Sec. III.E), with NLSM 2S scaling checked only through 10 points (Sec. III.D). Claims 2–5 impose these laws as defining constraints on arbitrary-n local ansätze; if a higher-multiplicity amplitude violated the assumed O(z^k) behavior for some δ, the constraints would not contain the true amplitude and the claimed uniqueness would fail. The claims should either be accompanied by an all-n proof of the scaling laws, or be restated as conditional results with the verification order made explicit.
  2. [Sec. V.C; Claim 4; Conjecture 1] The sGal uniqueness theorem is not self-contained: it assumes Conjecture 1, that the Galileon vertex is uniquely fixed by mass dimension [2n-2], SHS O(z^4), and 2S O(z^2). The paper verifies Conjecture 1 only through n=7 and provides no proof. Since the proof of Claim 4 uses Conjecture 1 both to identify any allowed contact term as the Galileon vertex and to exclude it via its SHS behavior, the claim is not established beyond n=7. The finite verification range should be stated explicitly in the theorem, and the proof of Conjecture 1 or a precise conditional statement is needed.
  3. [Sec. V.D; Appendix VIII.B] The proof of Claim 5 depends on the lemma that no polynomial of mass dimension [n] can have double-soft O(τ^3) scaling. Appendix VIII.B does not actually prove this lemma; after tensorizing, it asserts that no cancellations can occur 'in arbitrarily high dimensions, which is obvious.' That assertion is not demonstrated. A complete linear-algebra argument is needed, since this lemma is what rules out the higher double-soft orders in the BI contact-term analysis. As written, the BI uniqueness theorem is not fully proven. Similarly, the conclusion after Eq. (103) that verifying through τ^2 is sufficient because of 'arguments of the type given in ref. [14]' is a citation rather than a proof for all n.
minor comments (6)
  1. [Sec. III.C] The symbol σ denotes both the soft-scaling exponent in Eq. (50) and permutation labels throughout the paper; a different symbol would remove ambiguity.
  2. [First page header] The word 'theor ies' in the header should read 'theories'.
  3. [Sec. V.B] The induction excluding NLSM contact terms is terse; expanding the step from 'C_{n+1} scales as O(τ)' to 'ruled out by Adler-zero uniqueness' would make the argument easier to follow.
  4. [Sec. V.E] The double-copy scaling derivation assumes the NLSM and YM SHS/2S scalings; the text should say explicitly that this does not supply the missing all-multiplicity proof of those scalings.
  5. [Sec. VI] The list of quantities fixed by UV conditions mixes proven claims, conditional claims, and finite-order checks (Galileon vertex through n=7, sGal through n=6, BI through n=6, DBI-VA through n=8); adding the verification order to each bullet would avoid overstating the results.
  6. [Eqs. (69)–(71)] The 'or better' clauses make the stated scaling axioms non-sharp; the authors might specify the minimal set of inequalities actually used in the induction.

Circularity Check

0 steps flagged · score 0.0 of 10

No by-construction circularity: the UV-sufficiency claims are genuine constraint-satisfaction results, with the main caveats being unproven all-multiplicity scaling laws and an explicitly conjectural Galileon-vertex uniqueness step.

full rationale

The derivation chain does not define its outputs through its inputs. The UV scaling laws (e.g., Eqs. (60)-(63), (66)-(67), and (69)-(71)) are first established from known low-multiplicity amplitudes and then imposed as constraints on local ansaetze; solving for the unique ansatz satisfying those constraints is not equivalent to inserting the target amplitude into the input. Claim 1 reduces NLSM uniqueness from the BCJ relation to the independently established Adler-zero uniqueness of refs. [1,2,8]; that lemma is parameter-free and its assumptions (soft behavior, locality, mass dimension) do not include the BCJ or UV statements being derived, so the use is a legitimate modular reduction rather than a circular import. Claims 3 and 5 likewise invoke the prior soft-limit and soft-theorem uniqueness results [1,2,14] only after showing that the offending contact terms would inherit soft limits ruled out by those results. Claim 4 is explicitly conditional on Conjecture 1, which the paper labels as a conjecture verified only through n=7; the single-hard scalings for YM and NLSM are likewise explicitly verified only through n=7 and n=10, as stated in Sec. III.E: 'In the single-hard scaling case we do not have all multiplicity Yang-Mills or NLSM single-hard scaling arguments available, and so explicitly verified Yang-Mills through n = 7 and NLSM through n = 10.' These are genuine gaps in the sufficiency proof at arbitrary multiplicity and should be weighed as correctness or completeness risks, but they are not cases where a conclusion is assumed by construction or where a fitted parameter is renamed as a prediction. The self-citations to prior uniqueness theorems are load-bearing, but they refer to independent, checkable results whose assumptions do not contain the present targets, so under the review rules they do not constitute circularity.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No numerical constants are fitted to data; the free coefficients in the local ansätze are unknowns that the constraints solve for. The central claims instead rest on imported soft-limit uniqueness theorems and on the paper's own scaling conjecture, which are listed as axioms.

assumptions (6)
  • domain assumption Locality: amplitudes are sums over cubic/quartic diagrams with only simple massless poles.
    Used throughout Section III.A to define the local ansatz B_n = Σ N_i/D_i.
  • domain assumption Unitarity: on each pole the amplitude factorizes into lower-point amplitudes.
    Section III.B, eq. (48), used in Claims 3, 4, and 5.
  • domain assumption Prior soft-limit uniqueness: the only local objects with enhanced single-soft limits are NLSM, DBI, the Galileon vertex, and sGal.
    Section III.C; imported from refs. [2,8,14], with the paper noting the Galileon cases are not rigorously proven.
  • domain assumption Arbitrarily large spacetime dimension D > n for ansatz independence.
    Section III.A, stated to maximize independence of kinematic invariants.
  • ad hoc to paper Conjecture 1: the Galileon vertex is uniquely fixed by mass dimension [2n-2] and the UV scaling behaviors SHS O(z^4) and 2S O(z^2).
    Section V.C; unproven, verified only through n = 7, and load-bearing for the sGal uniqueness claim (Claim 4).
  • ad hoc to paper The single-hard-scaling laws hold at all multiplicities with the specified powers.
    Section III.E; verified at low multiplicity only, with no all-multiplicity proof, yet imposed on arbitrary-n ansätze.

how reviews work

0 comments
Cite this review

Pith. "Pith review of UV considerations on scattering amplitudes in a web of theories." pith.science (2026). https://pith.science/paper/2UTERNGT

@misc{pith2026190808033,
  author       = {Pith},
  title        = {Pith review of: UV considerations on scattering amplitudes in a web of theories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2UTERNGT}},
  note         = {Machine review of arXiv:1908.08033}
}
read the original abstract

The scattering predictions of a web of theories including Yang-Mills (YM), gravity, bi-adjoint scalar, the non-linear sigma model (NLSM), Dirac-Born-Infeld-Volkov-Akulov (DBI-VA) and the special Galileon (sGal) form a class of special objects with two fascinating properties: they are related by the double-copy procedure, and they can be defined purely by on-shell constraints. We expand on both of these properties. First we show that NLSM tree-level amplitudes are fully determined by imposing color-dual structure together with cyclic invariance and locality. We then consider how hard-scaling can be used to constrain the predictions of these theories, as opposed to the usual soft-scaling. We probe the UV by generalizing the familiar BCFW shift off-shell to a novel single hard limit. We show that UV scalings are sufficient to fully constrain: 1. Bi-adjoint doubly-ordered amplitudes, assuming locality; 2. NLSM and BI, assuming locality and unitarity; 3. Special Galileon, assuming locality, unitarity, and a UV bound for the general Galileon vertex. We see how potentially distinct aspects of this UV behavior can be understood and unified via double-copy relations. Surprisingly, we find evidence that assuming unitarity for these theories may not be necessary, and can emerge via UV considerations and locality alone. These results complete the observations that, like IR considerations, UV scaling is sufficient to fully constrain a wide range of tree-level amplitudes, for both gauge, gravity, and effective field theories.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Gravity loop integrands from the ultraviolet

    hep-th 2019-09 conditional novelty 7.0 of 10

    Four-dimensional N=8 supergravity loop integrands scale one power better at infinity than general-D power-counting predicts, and this homogeneous scaling combined with BCFW behavior uniquely fixes the integrand throug...

Reference graph

Works this paper leans on

144 extracted references · 9 canonical work pages · cited by 1 Pith paper

  1. [14]

    S. L. Adler, Consistency conditions on the strong interactions implied b y a partially conserved axial vector current , Phys. Rev. 137 (1965) B1022

    1965

  2. [1]

    supersymmetric DBI-V A : NLSM ⊗ supersymmetric Yang-Mills

  3. [2]

    bad” and “good

    Special Galileon: NLSM ⊗ NLSM Each of these theories has diverging high-energy behavior and so c an be understood as effective field theories requiring some sort of completion in the UV. The NLSM itself finds a UV completion in abelian Z-theory [79] and the (supersymmetr ic) DBI-V A has a UV completion in the abelian supersymmetric open-string. While each of...

  4. [3]

    The special Galileon amplitude (verified through 6 points)

  5. [4]

    Supersymmetric DBI-VA The UV constraints can be applied to 4D kinematics as well. We find that the photon and fermion sectors of DBI-V A in four dimensions are uniquely fixed by loc ality, mass dimension, helicity weight, and two particle shift scalings: Aphoton ∼ { O(z0) for ( −, −), (+, +) and ( −, +) (104) O(z4) for (+ , −) (105) Afermion ∼       ...

  6. [5]

    NLSM amplitudes (verified through 8 points)

  7. [6]

    The Galileon vertex (verified through 7 points)

  8. [7]

    Arkani-Hamed, F

    N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory? , JHEP 09 (2010) 016 [ 0808.1446]

    arXiv 2010

Show all 144 references
  1. [8]

    Arbitrary dimension Born-Infeld (verified through 6 points)

  2. [9]

    Amplituhedron

    4D Supersymmetric DBI-V A vector and fermion amplitudes (verifi ed through 8 points). These results extend the list of cases when amplitudes can be derive d solely from new principles. This makes it increasingly plausible that a different formulat ion exists, where some of these...

  3. [10]

    Arkani-Hamed, L

    N. Arkani-Hamed, L. Rodina and J. Trnka, Locality and unitarity of scattering amplitudes from singularities and gauge invariance , Phys. Rev. Lett. 120 (2018) 231602 [ 1612.02797]

    2018 arXiv

  4. [11]

    Rodina, Uniqueness from gauge invariance and the Adler zero , 1612.06342

    L. Rodina, Uniqueness from gauge invariance and the Adler zero , 1612.06342

    arXiv

  5. [12]

    Susskind and G

    L. Susskind and G. Frye, Algebraic aspects of pionic duality diagrams , Phys. Rev. D1 (1970) 1682

    1970

  6. [13]

    Osborn, Implications of adler zeros for multipion processes , Lett

    H. Osborn, Implications of adler zeros for multipion processes , Lett. Nuovo Cim. 2S1 (1969) 717

    1969

  7. [15]

    J. R. Ellis and B. Renner, On the relationship between chiral and dual models , Nucl. Phys. B21 (1970) 205

    1970

  8. [16]

    Benincasa and F

    P. Benincasa and F. Cachazo, Consistency Conditions on the S-Matrix of Massless Particles, 0705.4305

    arXiv

  9. [17]

    Cheung, K

    C. Cheung, K. Kampf, J. Novotny and J. Trnka, Effective Field Theories from Soft Limits of Scattering Amplitudes , Phys. Rev. Lett. 114 (2015) 221602 [ 1412.4095]

    2015 arXiv

  10. [18]

    Cheung, K

    C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A periodic table of effective field theories , JHEP 02 (2017) 020 [ 1611.03137]

    2017 arXiv

  11. [19]

    Cachazo and A

    F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem , 1404.4091

    arXiv

  12. [20]

    Strominger and A

    A. Strominger and A. Zhiboedov, Gravitational Memory, BMS Supertranslations and Soft Theorems, JHEP 01 (2016) 086 [ 1411.5745]

    2016 arXiv

  13. [21]

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

    2015 arXiv

  14. [22]

    S. W. Hawking, M. J. Perry and A. Strominger, Soft Hair on Black Holes , Phys. Rev. Lett. 116 (2016) 231301 [ 1601.00921]

    2016 arXiv

  15. [23]

    Rodina, Scattering amplitudes from soft theorems and infrared beha vior, Phys

    L. Rodina, Scattering amplitudes from soft theorems and infrared beha vior, Phys. Rev. Lett. 122 (2019) 071601 [ 1807.09738]

    2019 arXiv

  16. [24]

    Britto, F

    R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory , Phys. Rev. Lett. 94 (2005) 181602 [ hep-th/0501052]. 38

    2005 arXiv

  17. [25]

    Arkani-Hamed and J

    N. Arkani-Hamed and J. Kaplan, On Tree Amplitudes in Gauge Theory and Gravity , JHEP 04 (2008) 076 [ 0801.2385]

    2008 arXiv

  18. [26]

    D. A. McGady and L. Rodina, Higher-spin massless S-matrices in four-dimensions , Phys. Rev. D90 (2014) 084048 [ 1311.2938]

    2014 arXiv

  19. [27]

    Kampf, J

    K. Kampf, J. Novotny and J. Trnka, Tree-level amplitudes in the nonlinear sigma model , JHEP 05 (2013) 032 [ 1304.3048]

    2013 arXiv

  20. [28]

    Kampf, J

    K. Kampf, J. Novotny and J. Trnka, Recursion relations for tree-level amplitudes in the SU (N ) nonlinear sigma model , Phys. Rev. D87 (2013) 081701 [ 1212.5224]

    2013 arXiv

  21. [29]

    Cheung, C.-H

    C. Cheung, C.-H. Shen and J. Trnka, Simple Recursion Relations for General Field Theories, JHEP 06 (2015) 118 [ 1502.05057]

    2015 arXiv

  22. [30]

    Luo and C

    H. Luo and C. Wen, Recursion relations from soft theorems , JHEP 03 (2016) 088 [1512.06801]

    2016 arXiv

  23. [31]

    Cachazo, P

    F. Cachazo, P. Cha and S. Mizera, Extensions of theories from soft limits , JHEP 06 (2016) 170 [ 1604.03893]

    2016 arXiv

  24. [32]

    Low and Z

    I. Low and Z. Yin, Soft Bootstrap and Effective Field Theories , 1904.12859

    1904 arXiv

  25. [33]

    Elvang, M

    H. Elvang, M. Hadjiantonis, C. R. T. Jones and S. Paranja pe, Soft Bootstrap and Supersymmetry, JHEP 01 (2019) 195 [ 1806.06079]

    2019 arXiv

  26. [34]

    Cachazo, S

    F. Cachazo, S. He and E. Y. Yuan, Scattering equations and matrices: From Einstein to Yang-Mills, DBI and NLSM , JHEP 07 (2015) 149 [ 1412.3479]

    2015 arXiv

  27. [35]

    Rodina, Uniqueness from locality and BCFW shifts , 1612.03885

    L. Rodina, Uniqueness from locality and BCFW shifts , 1612.03885

    arXiv

  28. [36]

    Z. Bern, J. J. M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes , Phys. Rev. D78 (2008) 085011 [ 0805.3993]

    2008 arXiv

  29. [37]

    Z. Bern, J. J. M. Carrasco and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory , Phys. Rev. Lett. 105 (2010) 061602 [ 1004.0476]

    2010 arXiv

  30. [38]

    Kawai, D

    H. Kawai, D. C. Lewellen and S. H. H. Tye, A relation between tree amplitudes of closed and open strings , Nucl. Phys. B269 (1986) 1

    1986

  31. [39]

    Cachazo, S

    F. Cachazo, S. He and E. Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D90 (2014) 065001 [ 1306.6575]

    2014 arXiv

  32. [40]

    Cachazo, S

    F. Cachazo, S. He and E. Y. Yuan, Scattering of massless particles in arbitrary dimensions , Phys. Rev. Lett. 113 (2014) 171601 [ 1307.2199]. 39

    2014 arXiv

  33. [41]

    Cachazo, S

    F. Cachazo, S. He and E. Y. Yuan, Scattering of massless particles: scalars, gluons and gravitons, JHEP 07 (2014) 033 [ 1309.0885]

    2014 arXiv

  34. [42]

    Cachazo, S

    F. Cachazo, S. He and E. Y. Yuan, Einstein-Yang-Mills scattering amplitudes from scattering equations, JHEP 01 (2015) 121 [ 1409.8256]

    2015 arXiv

  35. [43]

    Anastasiou, L

    A. Anastasiou, L. Borsten, M. J. Duff, L. J. Hughes and S. Na gy, Yang-Mills origin of gravitational symmetries, Phys. Rev. Lett. 113 (2014) 231606 [ 1408.4434]

    2014 arXiv

  36. [44]

    He and Y

    S. He and Y. Zhang, New Formulas for Amplitudes from Higher-Dimensional Opera tors, JHEP 02 (2017) 019 [ 1608.08448]

    2017 arXiv

  37. [45]

    Cheung, C.-H

    C. Cheung, C.-H. Shen and C. Wen, Unifying relations for scattering amplitudes , JHEP 02 (2018) 095 [ 1705.03025]

    2018 arXiv

  38. [46]

    soft factors

    1 s123 + perms. (37) The general dimension BI amplitudes can be laborious to write out eve n at four points, but they can be given by: ABI 4 =stAYM 4 = [ 4Tr(F1F2F3F4) − Tr(F1F2)Tr(F3F4) + cyclic(1, 2, 3) ] . (38) 13 The traces are over Lorentz indices of linearized momentum-s...

  39. [47]

    Cheung, G

    C. Cheung, G. N. Remmen, C.-H. Shen and C. Wen, Pions as gluons in higher dimensions , JHEP 04 (2018) 129 [ 1709.04932]

    2018 arXiv

  40. [48]

    Z. Bern, J. J. Carrasco, W.-M. Chen, H. Johansson and R. R oiban, Gravity amplitudes as generalized double copies of gauge-theory amplitudes , Phys. Rev. Lett. 118 (2017) 181602 [1701.02519]

    2017 arXiv

  41. [49]

    Z. Bern, J. J. Carrasco, W.-M. Chen, A. Edison, H. Johans son, J. Parra-Martinez et al., Ultraviolet Properties of N = 8 Supergravity at Five Loops , Phys. Rev. D98 (2018) 086021 [1804.09311]

    2018 arXiv

  42. [50]

    R. H. Boels, B. A. Kniehl, O. V. Tarasov and G. Yang, Color-kinematic duality for form factors, JHEP 02 (2013) 063 [ 1211.7028]

    2013 arXiv

  43. [51]

    Yang, Color-kinematics duality and Sudakov form factor at five loop s for N = 4 supersymmetric Yang-Mills theory , Phys

    G. Yang, Color-kinematics duality and Sudakov form factor at five loop s for N = 4 supersymmetric Yang-Mills theory , Phys. Rev. Lett. 117 (2016) 271602 [ 1610.02394]

    2016 arXiv

  44. [52]

    Borsten, M

    L. Borsten, M. J. Duff, L. J. Hughes and S. Nagy, Magic square from Yang-Mills squared , Phys. Rev. Lett. 112 (2014) 131601 [ 1301.4176]

    2014 arXiv

  45. [53]

    Nagy, Chiral squaring , JHEP 07 (2016) 142 [ 1412.4750]

    S. Nagy, Chiral squaring , JHEP 07 (2016) 142 [ 1412.4750]

    2016 arXiv

  46. [54]

    Anastasiou, L

    A. Anastasiou, L. Borsten, M. J. Hughes and S. Nagy, Global symmetries of Yang-Mills squared in various dimensions , JHEP 01 (2016) 148 [ 1502.05359]

    2016 arXiv

  47. [55]

    Cardoso, S

    G. Cardoso, S. Nagy and S. Nampuri, Multi-centered N = 2 BPS black holes: a double copy description, JHEP 04 (2017) 037 [ 1611.04409]. 40

    2017 arXiv

  48. [56]

    G. L. Cardoso, S. Nagy and S. Nampuri, A double copy for N = 2 supergravity: a linearised tale told on-shell , JHEP 10 (2016) 127 [ 1609.05022]

    2016 arXiv

  49. [57]

    Anastasiou, L

    A. Anastasiou, L. Borsten, M. J. Duff, S. Nagy and M. Zoccal i, Gravity as gauge theory squared: A ghost story , Phys. Rev. Lett. 121 (2018) 211601 [ 1807.02486]

    2018 arXiv

  50. [58]

    Neill and I

    D. Neill and I. Z. Rothstein, Classical space-times from the S matrix , Nucl. Phys. B877 (2013) 177 [ 1304.7263]

    2013 arXiv

  51. [59]

    Monteiro, D

    R. Monteiro, D. O’Connell and C. D. White, Black holes and the double copy , JHEP 12 (2014) 056 [ 1410.0239]

    2014 arXiv

  52. [60]

    A. Luna, R. Monteiro, D. O’Connell and C. D. White, The classical double copy for Taub–NUT spacetime, Phys. Lett. B750 (2015) 272 [ 1507.01869]

    2015 arXiv

  53. [61]

    A. K. Ridgway and M. B. Wise, Static spherically symmetric Kerr-Schild metrics and implications for the classical double copy , Phys. Rev. D94 (2016) 044023 [ 1512.02243]

    2016 arXiv

  54. [62]

    A. Luna, R. Monteiro, I. Nicholson, D. O’Connell and C. D . White, The double copy: Bremsstrahlung and accelerating black holes , JHEP 06 (2016) 023 [ 1603.05737]

    2016 arXiv

  55. [63]

    A. Luna, R. Monteiro, I. Nicholson, A. Ochirov, D. O’Con nell, N. Westerberg et al., Perturbative spacetimes from Yang-Mills theory , JHEP 04 (2017) 069 [ 1611.07508]

    2017 arXiv

  56. [64]

    C. D. White, Exact solutions for the biadjoint scalar field , Phys. Lett. B763 (2016) 365 [1606.04724]

    2016 arXiv

  57. [65]

    A. Luna, R. Monteiro, I. Nicholson and D. O’Connell, Type D spacetimes and the Weyl double copy, 1810.08183

    arXiv

  58. [66]

    A. Luna, I. Nicholson, D. O’Connell and C. D. White, Inelastic black hole scattering from charged scalar amplitudes , JHEP 03 (2018) 044 [ 1711.03901]

    2018 arXiv

  59. [67]

    W. D. Goldberger, S. G. Prabhu and J. O. Thompson, Classical gluon and graviton radiation from the bi-adjoint scalar double copy , Phys. Rev. D96 (2017) 065009 [1705.09263]

    2017 arXiv

  60. [68]

    W. D. Goldberger and A. K. Ridgway, Radiation and the classical double copy for color charges, Phys. Rev. D95 (2017) 125010 [ 1611.03493]

    2017 arXiv

  61. [69]

    W. D. Goldberger and A. K. Ridgway, Bound states and the classical double copy , Phys. Rev. D97 (2018) 085019 [ 1711.09493]

    2018 arXiv

  62. [70]

    Carrillo-Gonz´ alez, R

    M. Carrillo-Gonz´ alez, R. Penco and M. Trodden, The classical double copy in maximally symmetric spacetimes, JHEP 04 (2018) 028 [ 1711.01296]. 41

    2018 arXiv

  63. [71]

    Gurses and B

    M. Gurses and B. Tekin, Classical double copy: Kerr-Schild-Kundt metrics from Yang -Mills theory, Phys. Rev. D98 (2018) 126017 [ 1810.03411]

    2018 arXiv

  64. [72]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon and M. Zeng, Scattering amplitudes and the conservative Hamiltonian for binary sys tems at third post-Minkowskian order, 1901.04424

    1901 arXiv

  65. [73]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon and M. Zeng, Black Hole Binary Dynamics from the Double Copy and Effective Theory , 1908.01493

    1908 arXiv

  66. [74]

    Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The Duality Between Color and Kinematics and its Applications , 1909.01358

    1909 arXiv

  67. [75]

    Z. Bern, A. De Freitas and H. L. Wong, On the coupling of gravitons to matter , Phys. Rev. Lett. 84 (2000) 3531 [ hep-th/9912033]

    2000 arXiv

  68. [76]

    Y.-J. Du, B. Feng and C.-H. Fu, BCJ relation of color scalar theory and KLT relation of gauge theory, JHEP 08 (2011) 129 [ 1105.3503]

    2011 arXiv

  69. [77]

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, R. Monteiro and D. O’Connell, Algebras for amplitudes, JHEP 06 (2012) 061 [ 1203.0944]

    2012 arXiv

  70. [78]

    Chiodaroli, M

    M. Chiodaroli, M. G¨ unaydin, H. Johansson and R. Roiban , Scattering amplitudes in N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity , JHEP 01 (2015) 081 [ 1408.0764]

    2015 arXiv

  71. [79]

    Chiodaroli, M

    M. Chiodaroli, M. Gunaydin, H. Johansson and R. Roiban, Spontaneously broken Yang-Mills-Einstein supergravities as double copies , JHEP 06 (2017) 064 [ 1511.01740]

    2017 arXiv

  72. [80]

    Low and Z

    I. Low and Z. Yin, Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models, Phys. Rev. Lett. 120 (2018) 061601 [ 1709.08639]

    2018 arXiv

  73. [81]

    Del Duca, L

    V. Del Duca, L. J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level , Nucl. Phys. B571 (2000) 51 [ hep-ph/9910563]

    2000 arXiv

  74. [82]

    Mizera, Inverse of the string theory KLT kernel , JHEP 06 (2017) 084 [ 1610.04230]

    S. Mizera, Inverse of the string theory KLT kernel , JHEP 06 (2017) 084 [ 1610.04230]

    2017 arXiv

  75. [83]

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, B. Feng and T. Sond ergaard, Gravity and Yang-Mills amplitude relations , Phys. Rev. D82 (2010) 107702 [ 1005.4367]

    2010 arXiv

  76. [84]

    J. A. Cronin, Phenomenological model of strong and weak interactions in c hiral U(3) x U(3), Phys. Rev. 161 (1967) 1483

    1967

  77. [85]

    Weinberg, Dynamical approach to current algebra , Phys

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

    1967

  78. [86]

    Weinberg, Nonlinear realizations of chiral symmetry , Phys

    S. Weinberg, Nonlinear realizations of chiral symmetry , Phys. Rev. 166 (1968) 1568. 42

    1968

  79. [87]

    A. J. MacFarlane, A. Sudbery and P. H. Weisz, On gell-mann ’sλ-matrices, d- and f -tensors, octets, and parametrizations of su(3), Comm. Math. Phys. 11 (1968) 77

    1968

  80. [88]

    J. J. M. Carrasco, C. R. Mafra and O. Schlotterer, Abelian Z-theory: NLSM amplitudes and α’-corrections from the open string , JHEP 06 (2017) 093 [ 1608.02569]

    2017 arXiv

  81. [89]

    Low and Z

    I. Low and Z. Yin, The infrared structure of Nambu-Goldstone bosons , JHEP 10 (2018) 078 [1804.08629]

    2018 arXiv

  82. [90]

    Bagger and A

    J. Bagger and A. Galperin, A New Goldstone multiplet for partially broken supersymmet ry, Phys. Rev. D55 (1997) 1091 [ hep-th/9608177]

    1997 arXiv

  83. [91]

    Bergshoeff, F

    E. Bergshoeff, F. Coomans, R. Kallosh, C. S. Shahbazi and A . Van Proeyen, Dirac-Born-Infeld-Volkov-Akulov and deformation of super symmetry, JHEP 08 (2013) 100 [1303.5662]

    2013 arXiv

  84. [92]

    Cheung, K

    C. Cheung, K. Kampf, J. Novotny, C.-H. Shen, J. Trnka and C. Wen, Vector effective field theories from soft limits , Phys. Rev. Lett. 120 (2018) 261602 [ 1801.01496]

    2018 arXiv

  85. [93]

    G. R. Dvali, G. Gabadadze and M. Porrati, 4-D gravity on a brane in 5-D Minkowski space , Phys. Lett. B485 (2000) 208 [ hep-th/0005016]

    2000 arXiv

  86. [94]

    Nicolis, R

    A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity , Phys. Rev. D79 (2009) 064036 [ 0811.2197]

    2009 arXiv

  87. [95]

    de Rham, G

    C. de Rham, G. Gabadadze and A. J. Tolley, Resummation of Massive Gravity , Phys. Rev. Lett. 106 (2011) 231101 [ 1011.1232]

    2011 arXiv

  88. [96]

    Kampf and J

    K. Kampf and J. Novotny, Unification of Galileon Dualities , JHEP 10 (2014) 006 [1403.6813]

    2014 arXiv

  89. [97]

    Hinterbichler and A

    K. Hinterbichler and A. Joyce, Hidden symmetry of the Galileon , Phys. Rev. D92 (2015) 023503 [ 1501.07600]

    2015 arXiv

  90. [98]

    Novotny, Geometry of special Galileons , Phys

    J. Novotny, Geometry of special Galileons , Phys. Rev. D95 (2017) 065019 [ 1612.01738]

    2017 arXiv

  91. [99]

    He, Y.-t

    S. He, Y.-t. Huang and C. Wen, Loop Corrections to Soft Theorems in Gauge Theories and Gravity, JHEP 12 (2014) 115 [ 1405.1410]

    2014 arXiv

  92. [100]

    S. He, Z. Liu and J.-B. Wu, Scattering equations, twistor-string formulas and double -soft limits in four dimensions , JHEP 07 (2016) 060 [ 1604.02834]

    2016 arXiv

  93. [101]

    A. L. Guerrieri, Y.-t. Huang, Z. Li and C. Wen, On the exactness of soft theorems , JHEP 12 (2017) 052 [ 1705.10078]. 43

    2017 arXiv

  94. [102]

    Z. Bern, S. Davies, P. Di Vecchia and J. Nohle, Low-energy behavior of gluons and gravitons from gauge invariance , Phys. Rev. D90 (2014) 084035 [ 1406.6987]

    2014 arXiv

  95. [103]

    Z. Bern, S. Davies and J. Nohle, On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons , Phys. Rev. D90 (2014) 085015 [ 1405.1015]

    2014 arXiv

  96. [104]

    Huang and C

    Y.-t. Huang and C. Wen, Soft theorems from anomalous symmetries , JHEP 12 (2015) 143 [1509.07840]

    2015 arXiv

  97. [105]

    Chen, Y.-t

    W.-M. Chen, Y.-t. Huang and C. Wen, New Fermionic Soft Theorems for Supergravity Amplitudes, Phys. Rev. Lett. 115 (2015) 021603 [ 1412.1809]

    2015 arXiv

  98. [106]

    Low, Double Soft Theorems and Shift Symmetry in Nonlinear Sigma Mo dels, Phys

    I. Low, Double Soft Theorems and Shift Symmetry in Nonlinear Sigma Mo dels, Phys. Rev. D93 (2016) 045032 [ 1512.01232]

    2016 arXiv

  99. [107]

    Elvang, C

    H. Elvang, C. R. T. Jones and S. G. Naculich, Soft photon and graviton theorems in effective field theory , Phys. Rev. Lett. 118 (2017) 231601 [ 1611.07534]

    2017 arXiv

  100. [108]

    Di Vecchia, R

    P. Di Vecchia, R. Marotta, M. Mojaza and J. Nohle, New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading o rder, Phys. Rev. D93 (2016) 085015 [ 1512.03316]

    2016 arXiv

  101. [109]

    Di Vecchia, R

    P. Di Vecchia, R. Marotta and M. Mojaza, Soft theorem for the graviton, dilaton and the Kalb-Ramond field in the bosonic string , JHEP 05 (2015) 137 [ 1502.05258]

    2015 arXiv

  102. [110]

    B. U. W. Schwab and A. Volovich, Subleading Soft Theorem in Arbitrary Dimensions from Scattering Equations, Phys. Rev. Lett. 113 (2014) 101601 [ 1404.7749]

    2014 arXiv

  103. [111]

    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

    arXiv

  104. [112]

    Cachazo, S

    F. Cachazo, S. He and E. Y. Yuan, New Double Soft Emission Theorems , Phys. Rev. D92 (2015) 065030 [ 1503.04816]

    2015 arXiv

  105. [113]

    He and Q

    S. He and Q. Yang, An Etude on Recursion Relations and Triangulations , JHEP 05 (2019) 040 [ 1810.08508]

    2019 arXiv

  106. [114]

    Benincasa, C

    P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming Tree Amplitudes In General Relativity, JHEP 11 (2007) 057 [ hep-th/0702032]

    2007 arXiv

  107. [115]

    P. C. Schuster and N. Toro, Constructing the Tree-Level Yang-Mills S-Matrix Using Complex Factorization, JHEP 06 (2009) 079 [ 0811.3207]

    2009 arXiv

  108. [116]

    R. H. Boels and R. Medina, Graviton and gluon scattering from first principles , Phys. Rev. Lett. 118 (2017) 061602 [ 1607.08246]. 44

    2017 arXiv

  109. [117]

    Cachazo, P

    F. Cachazo, P. Svrcek and E. Witten, MHV vertices and tree amplitudes in gauge theory , JHEP 09 (2004) 006 [ hep-th/0403047]

    2004 arXiv

  110. [118]

    F. A. Berends and W. T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys. B306 (1988) 759

    1988

  111. [119]

    S. Lee, C. R. Mafra and O. Schlotterer, Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality , JHEP 03 (2016) 090 [ 1510.08843]

    2016 arXiv

  112. [120]

    C. R. Mafra, Berends-Giele recursion for double-color-ordered amplit udes, JHEP 07 (2016) 080 [ 1603.09731]

    2016 arXiv

  113. [121]

    Mizera and B

    S. Mizera and B. Skrzypek, Perturbiner methods for effective field theories and the doub le copy, JHEP 10 (2018) 018 [ 1809.02096]

    2018 arXiv

  114. [122]

    Broedel, M

    J. Broedel, M. de Leeuw, J. Plefka and M. Rosso, Constraining subleading soft gluon and graviton theorems, Phys. Rev. D90 (2014) 065024 [ 1406.6574]

    2014 arXiv

  115. [123]

    Froissart, Asymptotic behavior and subtractions in the Mandelstam rep resentation, Phys

    M. Froissart, Asymptotic behavior and subtractions in the Mandelstam rep resentation, Phys. Rev. 123 (1961) 1053

    1961

  116. [124]

    Kleiss and H

    R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadro n colliders, Nucl. Phys. B312 (1989) 616

    1989

  117. [125]

    Chen and Y.-J

    G. Chen and Y.-J. Du, Amplitude relations in non-linear sigma model , JHEP 01 (2014) 061 [ 1311.1133]

    2014 arXiv

  118. [126]

    B. Feng, R. Huang and Y. Jia, Gauge amplitude identities by on-shell recursion relation in S-matrix program, Phys. Lett. B695 (2011) 350 [ 1004.3417]

    2011 arXiv

  119. [127]

    J. J. M. Carrasco, C. R. Mafra and O. Schlotterer, Semi-abelian Z-theory: NLSM +φ3 from the open string , JHEP 08 (2017) 135 [ 1612.06446]

    2017 arXiv

  120. [128]

    Caron-Huot, Z

    S. Caron-Huot, Z. Komargodski, A. Sever and A. Zhiboed ov, Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude , JHEP 10 (2017) 026 [1607.04253]

    2017 arXiv

  121. [129]

    D. A. McGady and L. Rodina, Recursion relations for graviton scattering amplitudes fr om Bose symmetry and bonus scaling laws , Phys. Rev. D91 (2015) 105010 [ 1408.5125]

    2015 arXiv

  122. [130]

    Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the square of gauge theory , Phys. Rev. D82 (2010) 065003 [ 1004.0693]

    2010 arXiv

  123. [131]

    R. H. Boels and R. S. Isermann, On powercounting in perturbative quantum gravity theories through color-kinematic duality , JHEP 06 (2013) 017 [ 1212.3473]. 45

    2013 arXiv

  124. [132]

    Arkani-Hamed and J

    N. Arkani-Hamed and J. Trnka, The amplituhedron, JHEP 10 (2014) 030 [ 1312.2007]

    2014 arXiv

  125. [133]

    Arkani-Hamed, Y

    N. Arkani-Hamed, Y. Bai, S. He and G. Yan, Scattering forms and the positive geometry of kinematics, color and the worldsheet , JHEP 05 (2018) 096 [ 1711.09102]

    2018 arXiv

  126. [134]

    Loebbert, M

    F. Loebbert, M. Mojaza and J. Plefka, Hidden conformal symmetry in tree-level graviton scattering, JHEP 05 (2018) 208 [ 1802.05999]

    2018 arXiv

  127. [135]

    J. L. Bourjaily, E. Herrmann and J. Trnka, Maximally supersymmetric amplitudes at infinite loop momentum , Phys. Rev. D99 (2019) 066006 [ 1812.11185]

    2019 arXiv

  128. [136]

    Caron-Huot and M

    S. Caron-Huot and M. Wilhelm, Renormalization group coefficients and the S-matrix , JHEP 12 (2016) 010 [ 1607.06448]

    2016 arXiv

  129. [137]

    Pasterski and S.-H

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

    2017 arXiv

  130. [138]

    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]

    2017 arXiv

  131. [139]

    Schreiber, A

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

    2018 arXiv

  132. [140]

    Donnay, A

    L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons , JHEP 01 (2019) 184 [ 1810.05219]

    2019 arXiv

  133. [141]

    Nandan, A

    D. Nandan, A. Schreiber, A. Volovich and M. Zlotnikov, Celestial Amplitudes: Conformal Partial Waves and Soft Limits , 1904.10940

    1904 arXiv

  134. [142]

    W. Fan, A. Fotopoulos and T. R. Taylor, Soft Limits of Yang-Mills Amplitudes and Conformal Correlators, JHEP 05 (2019) 121 [ 1903.01676]

    2019 arXiv

  135. [143]

    Guevara, Notes on Conformal Soft Theorems and Recursion Relations in Gr avity, 1906.07810

    A. Guevara, Notes on Conformal Soft Theorems and Recursion Relations in Gr avity, 1906.07810

    1906 arXiv

  136. [144]

    Stieberger and T

    S. Stieberger and T. R. Taylor, Strings on Celestial Sphere , Nucl. Phys. B935 (2018) 388 [1806.05688]. 46

    2018 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.