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Higher-spin effects in black hole and neutron star binary dynamics: worldline supersymmetry beyond minimal coupling

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that extending the supersymmetric worldline charge with non-minimal couplings fixed by supersymmetry closure produces all-order-in-spin Hamiltonians, a unique worldline criterion for Kerr geometry in four dimensions, and…

desk verdict New higher-spin worldline Hamiltonians and a genuinely useful framework, but the headline Kerr-uniqueness claim is an imposed-tracelessness conjecture, not a theorem. read the letter →

arxiv 2505.11488 v1 pith:IOOOK6WU submitted 2025-05-16 hep-th gr-qc

Domenico Bonocore , Anna Kulesza , Johannes Pirsch This is my paper · ORCID
classification hep-thgr-qc
keywords higher-spineffectsworldlinesupersymmetryKerrgeometrygravitationalwaveobservablesgeneralizedWilsonlinemassdipolepost-Minkowskianexpansiontidal
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

Worldline supersymmetric models are very efficient at capturing spin effects in black-hole and neutron-star binaries up to quadratic order in spin, but no-go theorems block higher orders. This paper proposes a way around the block: add a non-minimal coupling $q^\mu$ to the supersymmetry charge and require the algebra to close, i.e. solve $T_{ab}=0$ order by order in curvature and spin. The result is two new Hamiltonians: one that is all-order in spin and linear in curvature in four spacetime dimensions, containing every power of the mass dipole, and one that is cubic in spin in arbitrary dimensions, with two new tidal Wilson coefficients. The same construction yields a criterion, tracelessness of the couplings, that the authors claim uniquely selects the Kerr geometry, and a generalized Wilson line built from these Hamiltonians exponentiates the Kerr three-point and generic Compton amplitudes.

What carries the argument

The load-bearing object is the deformed supersymmetry charge $Q_i = i\psi^i_a e^a_\mu P^\mu$, with $P^\mu = \pi^\mu + q^\mu$, together with the closure equation $T_{ab}=0$ that encodes the supersymmetry algebra under Poisson brackets. Solving $T_{ab}=0$ for $q^\mu$ order by order in curvature and spin converts the problem of which higher-spin couplings are consistent into an algebraic solvability condition. The choice that makes the $d=4$ solution unique is the tracelessness condition $q_{\mu,(n)}\eta^{a_i a_j}=0$; this is imposed and then shown to fix all Wilson coefficients to unity, which is what selects Kerr. In generic dimensions the tracelessness condition is relaxed, and the residual freedom appears as the parameter $\mathcal{D}$ governing the new Wilson coefficients.

What would settle it

Solve the closure equation $T_{ab}=0$ at linear curvature in $d=4$ without imposing eq. (10) and compare solutions: a second solution whose Hamiltonian matches the Kerr multipole moments at $O(D^0)$ but differs at $O(D)$ would disprove the uniqueness claim. A supporting check would be to derive eq. (10) from requiring closure at second order in curvature; failure to do so would show the criterion is special to linear order.

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Extended reading notes

Core claim

The central claim is that supersymmetry on the worldline, if deformed beyond minimal coupling, does not stop at quadratic order in spin. Taking the charge $Q_i = i\psi^i_a e^a_\mu P^\mu$ with $P^\mu = \pi^\mu + q^\mu$ and imposing $\{Q_i,Q_j\}=0$ through $T_{ab}=0$ produces a tower of higher-spin Hamiltonians. In $d=4$ and at linear order in curvature the traceless solution is eq. (11): it is all-order in the spin and mass dipole, and its $O(D^0)$ part reduces to the known Kerr Hamiltonian in spin-vector form. In generic $d$ and at cubic order in spin, eq. (14) contains two new Wilson coefficients that cancel in $d=4$ and one free parameter $\mathcal{D}$, which the authors read as evidence that higher dimensions admit a family of Kerr-like solutions. Finally, the generalized Wilson line assembled from these Hamiltonians exponentiates the Kerr three-point amplitude and the three-point and Compton amplitudes for generic compact objects, making the eikonal phase and scattering angle computable.

Load-bearing premise

The paper's Kerr-selection result rests on the tracelessness condition $q_{\mu,(n)} \eta^{a_i a_j}=0$, imposed by hand in Section III.A: if another solution of the closure equation exists without that condition, the uniqueness of the Kerr geometry no longer follows.

Editorial extensions

If this is right

  • In four dimensions, eq. (11) supplies a manifestly supersymmetric Hamiltonian that is all-order in spin and includes all powers of the mass dipole, so 1PM observables can be computed without first choosing a spin supplementary condition.
  • The generic-dimensional cubic Hamiltonian (14) avoids Levi-Civita tensors, so it gives unambiguous integrands under dimensional regularization for 2PM higher-spin computations.
  • The generalized Wilson line result shows that the Kerr three-point amplitude exponentiates at all orders in spin, something that is non-trivial already at linear order in the amplitude approach.
  • The tidal Wilson coefficients $C_{ES^2}$, $\tilde{C}_{ES^2}$ and $C_{BS^3}$ exponentiate inside the eikonal phase, tying the finite-size structure of the body to resummed gravitational observables.
  • In $d=4$ all free coefficients collapse to unity through the tracelessness condition, giving a worldline derivation of Kerr multipole moments without inputting the Kerr solution by hand.

Reading between the lines

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

  • The paper does not prove that tracelessness is equivalent to the on-shell notion of minimal coupling for massive higher-spin particles; if that equivalence holds, the worldline algebra would provide a constructive definition of minimal coupling at all spin orders, and checking it directly is a natural next step.
  • Because eq. (11) keeps all mass-dipole orders, it suggests that SSC-independent observables can be formulated from the start, potentially removing a long-standing source of ambiguity in spinning-body dynamics.
  • A concrete extension is to solve eq. (8) at second order in curvature in $d=4$: if the traceless solution extends uniquely, the same criterion would determine the dynamical multipole moments of Kerr; if not, the Kerr-selection claim is specific to linear curvature.
  • The free parameter $\mathcal{D}$ in $d>4$ resembles the freedom used in neutron-star effective theories to encode tidal deformability; comparing the two could show whether the worldline algebra constrains only point-like Kerr dynamics or also the finite-size response of extended bodies.
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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 paper proposes extending N=2s supersymmetric worldline models for higher-spin particles by deforming the supercharge with a non-minimal coupling q\mu (eq. (4)). The central requirement is closure of the supersymmetry algebra, Tab=0 (eq. (8)). In d=4 and at linear order in the curvature, the authors claim a unique traceless solution q\mu that gives an all-order-in-spin Hamiltonian (eq. (11)) including all orders in the mass dipole D\mu; in generic d they present a cubic-in-spin Hamiltonian (eq. (14)) with new tidal Wilson coefficients. They further claim that in d=4 the tracelessness condition (eq. (10)) selects the Kerr multipole moments, and they construct Generalized Wilson Lines demonstrating exponentiation of the Kerr three-point amplitude and of the three-point and Compton amplitudes for generic compact objects.

Significance. If the derivations are made fully explicit, the results would be a valuable step beyond the no-go theorems for supersymmetric higher-spin worldlines: eq. (11) would provide a manifestly supersymmetric all-order-in-spin Hamiltonian with full mass-dipole dependence, and eq. (14) would give the first generic-d cubic-in-spin Hamiltonian with tidal structure suitable for dimensional regularization. The identifications with the known Kerr Hamiltonian and with d=4 results [78,102,112,90,117], together with the eikonal checks against [42,55,95], give non-trivial evidence that the constructed Hamiltonians are correct. The letter is clearly written and the novel GWL exponentiation results are well explained. However, the advertised uniqueness and the full construction of the solutions are not presented, and therefore the significance as currently stated is ahead of what is demonstrated in the manuscript.

major comments (4)
  1. [III.A, Eq. (11)] The authors state that eq. (10) makes Tab=0 'dramatically simplify' and then write down the Hamiltonian, but no derivation is given. Eq. (11) is therefore asserted as an ansatz rather than derived. Since this is the central new result, please provide the calculation (or an ancillary file) showing how the q\mu,(n) are constructed and how they satisfy eq. (8); at a minimum, display the first few q\mu,(n). This is load-bearing because eq. (11) is the main advertised new Hamiltonian.
  2. [Conclusions, third paragraph, and Section III.A] The statement 'we have shown that there exists a unique solution in d=4 to all orders in spin' is not supported by the text. Nothing in the manuscript proves that the traceless solution is the only solution to eq. (8), nor that eq. (10) follows from supersymmetry closure. Since Section III.B explicitly shows that relaxing tracelessness produces a family of solutions with a free parameter (eq. (16)), the uniqueness assertion is an overclaim. Please either provide a proof of uniqueness or restrict the claim to 'a solution that reproduces Kerr', which is the statement actually evidenced by the text.
  3. [III.B, Eq. (14)] The Hamiltonian in eq. (14) is obtained from 'an ansatz for q\mu,(n)' whose explicit form is not given; the coefficients CES2, \tilde{C}ES2, CBS3, and \tilde{C}BS3 are introduced only as 'shorthands' for combinations that are never displayed. Without this information the derivation is not reproducible. Please include the ansatz and the resulting expressions for all coefficients in an appendix or a supplementary file.
  4. [IV.A, Eq. (20)] The GWL exponentiation check is performed in the covariant SSC p\cdot\eta_i=0, which sets the mass dipole to zero. Consequently, eq. (20) tests only the D=0 (spin-vector) sector of eq. (11); the all-order-in-D terms that constitute 'all orders in the mass dipole' are not matched to any independent three-point amplitude. Please provide a cross-check for the D-dependent terms or state explicitly that this sector remains unchecked.
minor comments (5)
  1. [III.A, Eqs. (11)-(12)] Please define the symmetrization convention in E_{b1...bn-2,bn-1bn} and B_{b1...bn-2,bn-1bn} (e.g., how many terms are included) and clarify the parity convention for the exponents (-1)^{(3n-k)/2}.
  2. [III.B, Eqs. (14)-(16)] The free parameter D in eq. (16) clashes with the mass dipole D\mu used throughout the paper; please rename one of them to avoid confusion.
  3. [III.B, Eq. (15)] The term 'BDs' in eq. (15) is not defined; please spell out its form.
  4. [IV.B] The statement 'We have checked the eikonal and scattering angle against available results [42,55,95]' is not accompanied by any displayed comparison; please specify which observables, at which orders in G and S, and where the agreement is shown.
  5. [Throughout] There are several grammatical slips (e.g., 'This Hamiltonian is a new results', 'The all order in spin GWL is a new result') that should be corrected in a revised version.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the new Hamiltonians solve a supersymmetry-closure constraint and are checked against independent literature; the self-cited GWL framework is not load-bearing for the central derivation.

full rationale

The derivation chain is: deform the supersymmetry charge with q_mu (eq. (4)); impose closure T_ab = 0 (eq. (8)); impose the explicit tracelessness condition (eq. (10)); and write down a solution (eq. (11)). The tracelessness condition is an openly stated modeling assumption, not a condition defined in terms of the target Hamiltonian, so the Kerr result is not the input in another form. The output is benchmarked externally: the O(D^0) sector agrees with the known Kerr Hamiltonian [78,102,112] (eq. (13)), the d=4 cubic limit agrees with [90,117] (eq. (15)), and the eikonal and scattering angle are checked against [42,55,95]. No fitted parameter is renamed as a prediction: in generic d the Wilson coefficients are left as free parameters, including the unconstrained D in eq. (16). The GWL framework is taken from the authors' earlier papers [96,97], but this is a normal use of an established method and is not load-bearing for the supersymmetric derivation; the GWL results are also cross-checked against independent literature. The closest concern is a correctness issue rather than circularity: Section III.A writes 'a solution for q_mu can be written down', while the Conclusions claim 'there exists a unique solution in d = 4'; the displayed derivation does not prove uniqueness. That overclaim is not a circular reduction, because the traceless assumption is not constructed from the unique-Kerr result. Overall, no step in the claimed derivation is equivalent, by construction, to its own input.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The core derivation rests on the supersymmetry algebra and the imposed tracelessness condition. No new physical entities are introduced. In d=4, no free parameters remain; in generic d, one free parameter D survives. The GWL framework is self-cited but independently established.

free parameters (1)
  • D = unfixed (free)
    In the generic-d cubic Hamiltonian, the Wilson coefficients CES2, CES2 tilde, and CBS3 tilde depend on an unconstrained parameter D (eq. (16)). It is not fitted; the paper interprets it as reflecting the larger family of Kerr-like solutions in d>4.
assumptions (5)
  • domain assumption The N=2s supersymmetry algebra {Qi,Qj}_PB = -2i delta_ij H (eq. (1)) is the correct organizing principle for spin-s particles.
    Standard worldline formalism for spin; the paper extends it but assumes this algebra.
  • domain assumption The non-minimally coupled charge Qi = i psi^i e P_mu with q_mu expanded as a power series in the spin tensor (eqs. (4),(7)).
    This is the proposed deformation; the existence of such q_mu is assumed.
  • ad hoc to paper Tracelessness of q_mu,(n), eq. (10), is imposed to solve Tab=0 and select Kerr.
    Motivated by on-shell minimal coupling [110], but not derived from supersymmetry algebra; the Kerr uniqueness claim depends on it.
  • domain assumption The spin tensor is identified as S_mu_nu = i e e psi psi (eq. (3)) and the SSC is enforced by Qi=0.
    Standard identification in the worldline approach.
  • domain assumption The Generalized Wilson line path integral (eqs. (17)-(18)) computes the eikonal phase.
    Framework of the authors' prior work [96,97]; used as a tool for exponentiation.

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Cite this review

Pith. "Pith review of Higher-spin effects in black hole and neutron star binary dynamics: worldline supersymmetry beyond minimal coupling." pith.science (2026). https://pith.science/paper/IOOOK6WU

@misc{pith2026250511488,
  author       = {Pith},
  title        = {Pith review of: Higher-spin effects in black hole and neutron star binary dynamics: worldline supersymmetry beyond minimal coupling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IOOOK6WU}},
  note         = {Machine review of arXiv:2505.11488}
}
read the original abstract

The inclusion of spin effects in the binary dynamics for black hole and neutron stars is crucial for the computation of gravitational wave observables. Worldline supersymmetric models have shown to be particularly efficient at this task up to quadratic order in spin, but progress at higher orders has been hampered by no-go-theorems. In this work we propose a novel approach to overcome this problem by extending the supersymmetry beyond minimal coupling. We demonstrate the potential of this approach by computing an all-order in spin and linear in curvature, manifestly supersymmetric Hamiltonian, as well as a cubic order in spin Hamiltonian in arbitrary spacetime dimensions. In doing so, we identify a criterion that uniquely determines the Kerr geometry in terms of worldline supersymmetry. Equipped with these Hamiltonians, we demonstrate the exponentiation of three-point and Compton amplitudes using the recently proposed Generalized Wilson line approach.

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Forward citations

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Reference graph

Works this paper leans on

124 extracted references · 1 canonical work pages · cited by 2 Pith papers

  1. [90]

    Haddad, G

    K. Haddad, G. U. Jakobsen, G. Mogull, and J. Plefka, JHEP 02, 019, arXiv:2411.08176 [hep-th]

    arXiv

  2. [1]

    Punturo et al

    M. Punturo et al. , Class. Quant. Grav. 27, 194002 (2010)

    2010

  3. [2]

    Abac et al., (2025), arXiv:2503.12263 [gr-qc]

    A. Abac et al., (2025), arXiv:2503.12263 [gr-qc]

    arXiv 2025

  4. [3]

    Amaro-Seoane et al

    P. Amaro-Seoane et al. (LISA), (2017), arXiv:1702.00786 [astro-ph.IM]

    arXiv 2017

  5. [4]

    P. A. Seoane et al. (LISA), Living Rev. Rel.26, 2 (2023), arXiv:2203.06016 [gr-qc]

    arXiv 2023

  6. [5]

    B. P. Abbott et al. (LIGO Scientific), Class. Quant. Grav. 34, 044001 (2017), arXiv:1607.08697 [astro- ph.IM]

    arXiv 2017

  7. [6]

    Chamberlain and N

    K. Chamberlain and N. Yunes, Phys. Rev. D 96, 084039 (2017), arXiv:1704.08268 [gr-qc]

    arXiv 2017

  8. [7]

    S. W. Ballmer et al. , in Snowmass 2021 (2022) arXiv:2203.08228 [gr-qc]

    arXiv 2022

Show all 124 references
  1. [8]

    Damour, Phys

    T. Damour, Phys. Rev. D 97, 044038 (2018), arXiv:1710.10599 [gr-qc]

    2018 arXiv

  2. [9]

    Koemans Collado, P

    A. Koemans Collado, P. Di Vecchia, and R. Russo, Physical Review D 100, 10.1103/physrevd.100.066028 (2019)

    2019 doi

  3. [10]

    Mogull, J

    G. Mogull, J. Plefka, and J. Steinhoff, JHEP 02, 048, arXiv:2010.02865 [hep-th]

    2010 arXiv

  4. [11]

    Z. Bern, A. Luna, R. Roiban, C.-H. Shen, and M. Zeng, Phys. Rev. D 104, 065014 (2021), arXiv:2005.03071 [hep-th]

    2021 arXiv

  5. [12]

    Neill and I

    D. Neill and I. Z. Rothstein, Nucl. Phys. B 877, 177 (2013), arXiv:1304.7263 [hep-th]

    2013 arXiv

  6. [13]

    A. Luna, I. Nicholson, D. O’Connell, and C. D. White, JHEP 03, 044, arXiv:1711.03901 [hep-th]

    arXiv

  7. [14]

    D. A. Kosower, B. Maybee, and D. O’Connell, JHEP 02, 137, arXiv:1811.10950 [hep-th]

    arXiv

  8. [15]

    Cristofoli, R

    A. Cristofoli, R. Gonzo, D. A. Kosower, and D. O’Connell, Phys. Rev. D 106, 056007 (2022), arXiv:2107.10193 [hep-th]

    2022 arXiv

  9. [16]

    N. E. J. Bjerrum-Bohr, J. F. Donoghue, and P. Vanhove, JHEP 02, 111, arXiv:1309.0804 [hep-th]

    arXiv

  10. [17]

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Plant´ e, and P. Vanhove, Phys. Rev. Lett.121, 171601 (2018), arXiv:1806.04920 [hep-th]

    2018 arXiv

  11. [18]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 122, 201603 (2019), arXiv:1901.04424 [hep-th]

    2019 arXiv

  12. [19]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, JHEP 10, 206, arXiv:1908.01493 [hep-th]

    1908 arXiv

  13. [20]

    N. E. J. Bjerrum-Bohr, L. Plant´ e, and P. Vanhove, JHEP 03, 071, arXiv:2111.02976 [hep-th]

    arXiv

  14. [21]

    Cheung and M

    C. Cheung and M. P. Solon, JHEP 06, 144, arXiv:2003.08351 [hep-th]

    2003 arXiv

  15. [22]

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, L. Plant´ e, and P. Vanhove, JHEP 08, 172, arXiv:2105.05218 [hep-th]

    arXiv

  16. [23]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, Phys. Lett. B 811, 135924 (2020), arXiv:2008.12743 [hep-th]

    2020 arXiv

  17. [24]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, JHEP 07, 169, arXiv:2104.03256 [hep- th]

    arXiv

  18. [25]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, Phys. Lett. B 818, 136379 (2021), arXiv:2101.05772 [hep-th]

    2021 arXiv

  19. [26]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, Phys. Lett. B 843, 138049 (2023), arXiv:2210.12118 [hep-th]

    2023 arXiv

  20. [27]

    Heissenberg, Phys

    C. Heissenberg, Phys. Rev. Lett. 131, 011603 (2023), arXiv:2210.15689 [hep-th]

    2023 arXiv

  21. [28]

    G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, JHEP 10, 128, arXiv:2207.00569 [hep-th]

    arXiv

  22. [29]

    G. U. Jakobsen and G. Mogull, Phys. Rev. Lett. 128, 141102 (2022), arXiv:2201.07778 [hep-th]

    2022 arXiv

  23. [30]

    Bellazzini, G

    B. Bellazzini, G. Isabella, and M. M. Riva, JHEP 04, 023, arXiv:2211.00085 [hep-th]

    arXiv

  24. [31]

    Bastianelli, F

    F. Bastianelli, F. Comberiati, and L. de la Cruz, JHEP 02, 209, arXiv:2112.05013 [hep-th]

    arXiv

  25. [32]

    Damour, Phys

    T. Damour, Phys. Rev. D 102, 124008 (2020), arXiv:2010.01641 [gr-qc]

    2020 arXiv

  26. [33]

    Herrmann, J

    E. Herrmann, J. Parra-Martinez, M. S. Ruf, and M. Zeng, JHEP 10, 148, arXiv:2104.03957 [hep-th]

    arXiv

  27. [34]

    P. H. Damgaard, K. Haddad, and A. Helset, JHEP 11, 070, arXiv:1908.10308 [hep-ph]

    1908 arXiv

  28. [35]

    P. H. Damgaard, L. Plante, and P. Vanhove, JHEP 11, 213, arXiv:2107.12891 [hep-th]

    arXiv

  29. [36]

    P. H. Damgaard, E. R. Hansen, L. Plant´ e, and P. Van- hove, JHEP 09, 059, arXiv:2306.11454 [hep-th]

    arXiv

  30. [37]

    Aoude, K

    R. Aoude, K. Haddad, and A. Helset, JHEP 05, 051, arXiv:2001.09164 [hep-th]

    2001 arXiv

  31. [38]

    Accettulli Huber, A

    M. Accettulli Huber, A. Brandhuber, S. De Angelis, and G. Travaglini, Phys. Rev. D 103, 045015 (2021), arXiv:2012.06548 [hep-th]

    2021 arXiv

  32. [39]

    Brandhuber, G

    A. Brandhuber, G. Chen, G. Travaglini, and C. Wen, JHEP 10, 118, arXiv:2108.04216 [hep-th]

    arXiv

  33. [40]

    Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 126, 171601 (2021), arXiv:2101.07254 [hep-th]

    2021 arXiv

  34. [41]

    Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 128, 161103 (2022), arXiv:2112.10750 [hep-th]

    2022 arXiv

  35. [42]

    Z. Bern, D. Kosmopoulos, A. Luna, R. Roiban, and F. Teng, Phys. Rev. Lett. 130, 201402 (2023), arXiv:2203.06202 [hep-th]

    2023 arXiv

  36. [43]

    Z. Bern, D. Kosmopoulos, A. Luna, R. Roiban, T. Scheopner, F. Teng, and J. Vines, Phys. Rev. D 109, 045011 (2024), arXiv:2308.14176 [hep-th]

    2024 arXiv

  37. [44]

    P. H. Damgaard, E. R. Hansen, L. Plant´ e, and P. Van- hove, JHEP 09, 183, arXiv:2307.04746 [hep-th]

    arXiv

  38. [45]

    Brandhuber, G

    A. Brandhuber, G. R. Brown, G. Chen, S. De An- gelis, J. Gowdy, and G. Travaglini, JHEP 06, 048, arXiv:2303.06111 [hep-th]

    arXiv

  39. [46]

    Brandhuber, G

    A. Brandhuber, G. R. Brown, G. Chen, J. Gowdy, and G. Travaglini, JHEP02, 026, arXiv:2310.04405 [hep-th]

    arXiv

  40. [47]

    De Angelis, P

    S. De Angelis, P. P. Novichkov, and R. Gonzo, Phys. Rev. D 110, L041502 (2024), arXiv:2309.17429 [hep-th]

    2024 arXiv

  41. [48]

    Herderschee, R

    A. Herderschee, R. Roiban, and F. Teng, JHEP 06, 004, arXiv:2303.06112 [hep-th]

    arXiv

  42. [49]

    Caron-Huot, M

    S. Caron-Huot, M. Giroux, H. S. Hannesdottir, and S. Mizera, JHEP 01, 139, arXiv:2308.02125 [hep-th]

    arXiv

  43. [50]

    Febres Cordero, M

    F. Febres Cordero, M. Kraus, G. Lin, M. S. Ruf, and M. Zeng, Phys. Rev. Lett. 130, 021601 (2023), arXiv:2205.07357 [hep-th]

    2023 arXiv

  44. [51]

    Bohnenblust, H

    L. Bohnenblust, H. Ita, M. Kraus, and J. Schlenk, JHEP 11, 109, arXiv:2312.14859 [hep-th]

    arXiv

  45. [52]

    Z. Bern, E. Herrmann, R. Roiban, M. S. Ruf, A. V. Smirnov, V. A. Smirnov, and M. Zeng, JHEP 10, 023, arXiv:2406.01554 [hep-th]

  46. [53]

    Alaverdian, Z

    M. Alaverdian, Z. Bern, D. Kosmopoulos, A. Luna, 8 R. Roiban, T. Scheopner, and F. Teng, Phys. Rev. Lett. 134, 101602 (2025), arXiv:2407.10928 [hep-th]

    2025 arXiv

  47. [54]

    Akpinar, F

    D. Akpinar, F. Febres Cordero, M. Kraus, M. S. Ruf, and M. Zeng, JHEP 03, 126, arXiv:2407.19005 [hep-th]

    arXiv

  48. [55]

    Bohnenblust, L

    L. Bohnenblust, L. Cangemi, H. Johansson, and P. Pi- chini, (2024), arXiv:2410.23271 [hep-th]

    2024 arXiv

  49. [56]

    G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and Y. Xu, Phys. Rev. Lett. 131, 151401 (2023), arXiv:2306.01714 [hep-th]

    2023 arXiv

  50. [57]

    G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, Phys. Rev. Lett. 131, 241402 (2023), arXiv:2308.11514 [hep-th]

    2023 arXiv

  51. [58]

    Driesse, G

    M. Driesse, G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and J. Usovitsch, Phys. Rev. Lett.132, 241402 (2024), arXiv:2403.07781 [hep-th]

    2024 arXiv

  52. [59]

    Foffa, P

    S. Foffa, P. Mastrolia, R. Sturani, C. Sturm, and W. J. Torres Bobadilla, Phys. Rev. Lett. 122, 241605 (2019), arXiv:1902.10571 [gr-qc]

    2019 arXiv

  53. [60]

    Foffa and R

    S. Foffa and R. Sturani, Phys. Rev. D 100, 024047 (2019), arXiv:1903.05113 [gr-qc]

    2019 arXiv

  54. [61]

    Foffa, R

    S. Foffa, R. A. Porto, I. Rothstein, and R. Sturani, Phys. Rev. D 100, 024048 (2019), arXiv:1903.05118 [gr-qc]

    2019 arXiv

  55. [62]

    Adamo, R

    T. Adamo, R. Gonzo, and A. Ilderton, JHEP 05, 034, arXiv:2402.00124 [hep-th]

    arXiv

  56. [63]

    Akpinar, F

    D. Akpinar, F. Febres Cordero, M. Kraus, A. Smirnov, and M. Zeng, (2025), arXiv:2502.08961 [hep-th]

    2025 arXiv

  57. [64]

    Akpinar, V

    D. Akpinar, V. del Duca, and R. Gonzo, (2025), arXiv:2504.02025 [hep-th]

    2025

  58. [65]

    Beneke and V

    M. Beneke and V. A. Smirnov, Nucl. Phys. B 522, 321 (1998), arXiv:hep-ph/9711391

    1998 arXiv

  59. [66]

    Gehrmann and E

    T. Gehrmann and E. Remiddi, Nucl. Phys. B 580, 485 (2000), arXiv:hep-ph/9912329

    2000 arXiv

  60. [67]

    Laporta, Int

    S. Laporta, Int. J. Mod. Phys. A 15, 5087 (2000), arXiv:hep-ph/0102033

    2000 arXiv

  61. [68]

    A. V. Smirnov, JHEP 10, 107, arXiv:0807.3243 [hep- ph]

    arXiv

  62. [69]

    J. M. Henn, Phys. Rev. Lett. 110, 251601 (2013), arXiv:1304.1806 [hep-th]

    2013 arXiv

  63. [70]

    Klappert, F

    J. Klappert, F. Lange, P. Maierh¨ ofer, and J. Uso- vitsch, Comput. Phys. Commun. 266, 108024 (2021), arXiv:2008.06494 [hep-ph]

    2021 arXiv

  64. [71]

    Dlapa, J

    C. Dlapa, J. Henn, and K. Yan, JHEP 05, 025, arXiv:2002.02340 [hep-ph]

    2002 arXiv

  65. [72]

    Gardi, F

    E. Gardi, F. Herzog, S. Jones, and Y. Ma, JHEP 08, 127, arXiv:2407.13738 [hep-th]

    arXiv

  66. [73]

    de la Cruz, D

    L. de la Cruz, D. A. Kosower, and P. P. Novichkov, (2024), arXiv:2410.18014 [hep-th]

    2024 arXiv

  67. [74]

    K¨ alin and R

    G. K¨ alin and R. A. Porto, JHEP 01, 072, arXiv:1910.03008 [hep-th]

    1910 arXiv

  68. [75]

    K¨ alin and R

    G. K¨ alin and R. A. Porto, JHEP 02, 120, arXiv:1911.09130 [hep-th]

    1911 arXiv

  69. [76]

    G. Cho, G. K¨ alin, and R. A. Porto, JHEP04, 154, [Erra- tum: JHEP 07, 002 (2022)], arXiv:2112.03976 [hep-th]

    2022 arXiv

  70. [77]

    W. D. Goldberger and I. Z. Rothstein, Phys. Rev. D 73, 104029 (2006), arXiv:hep-th/0409156

    2006 arXiv

  71. [78]

    Levi and J

    M. Levi and J. Steinhoff, JHEP 09, 219, arXiv:1501.04956 [gr-qc]

    arXiv

  72. [79]

    K¨ alin and R

    G. K¨ alin and R. A. Porto, JHEP 11, 106, arXiv:2006.01184 [hep-th]

    2006 arXiv

  73. [80]

    Chung, Y.-t

    M.-Z. Chung, Y.-t. Huang, J.-W. Kim, and S. Lee, JHEP 05, 105, arXiv:2003.06600 [hep-th]

    2003 arXiv

  74. [81]

    Aoude, K

    R. Aoude, K. Haddad, and A. Helset, Phys. Rev. Lett. 129, 141102 (2022), arXiv:2205.02809 [hep-th]

    2022 arXiv

  75. [82]

    Alessio and P

    F. Alessio and P. Di Vecchia, Phys. Lett. B 832, 137258 (2022), arXiv:2203.13272 [hep-th]

    2022 arXiv

  76. [83]

    P. H. Damgaard, J. Hoogeveen, A. Luna, and J. Vines, Phys. Rev. D 106, 124030 (2022), arXiv:2208.11028 [hep-th]

    2022 arXiv

  77. [84]

    Chen, M.-Z

    W.-M. Chen, M.-Z. Chung, Y.-t. Huang, and J.-W. Kim, JHEP 08, 148, arXiv:2111.13639 [hep-th]

    arXiv

  78. [85]

    Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines, JHEP 03, 136, arXiv:2107.10179 [hep-th]

    arXiv

  79. [86]

    Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines, JHEP 05, 211, arXiv:2212.07965 [hep-th]

    arXiv

  80. [87]

    Guevara, A

    A. Guevara, A. Ochirov, and J. Vines, JHEP 09, 056, arXiv:1812.06895 [hep-th]

    arXiv

  81. [88]

    Cheung, J

    C. Cheung, J. Parra-Martinez, I. Z. Rothstein, N. Shah, and J. Wilson-Gerow, Phys. Rev. Lett. 132, 091402 (2024), arXiv:2308.14832 [hep-th]

    2024 arXiv

  82. [89]

    Ben-Shahar, JHEP 03, 108, arXiv:2311.01430 [hep- th]

    M. Ben-Shahar, JHEP 03, 108, arXiv:2311.01430 [hep- th]

    arXiv

  83. [91]

    N. E. J. Bjerrum-Bohr, G. Chen, C. Su, and T. Wang, (2025), arXiv:2503.20538 [hep-th]

    2025

  84. [92]

    Cipolletta, C

    F. Cipolletta, C. Cherubini, S. Filippi, J. A. Rueda, and R. Ruffini, Phys. Rev. D 92, 023007 (2015), arXiv:1506.05926 [astro-ph.SR]

    2015 arXiv

  85. [93]

    Maybee, D

    B. Maybee, D. O’Connell, and J. Vines, JHEP 12, 156, arXiv:1906.09260 [hep-th]

    1906 arXiv

  86. [94]

    Capatti and M

    Z. Capatti and M. Zeng, (2024), arXiv:2412.10864 [hep- th]

    2024 arXiv

  87. [95]

    G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff, JHEP 01, 027, arXiv:2109.04465 [hep-th]

    arXiv

  88. [96]

    Bonocore, A

    D. Bonocore, A. Kulesza, and J. Pirsch, JHEP 03, 147, arXiv:2112.02009 [hep-th]

    arXiv

  89. [97]

    Bonocore, A

    D. Bonocore, A. Kulesza, and J. Pirsch, JHEP 05, 034, arXiv:2412.16049 [hep-th]

    arXiv

  90. [98]

    Ajith, Y

    S. Ajith, Y. Du, R. Rajagopal, and D. Vaman, (2024), arXiv:2409.17866 [hep-th]

    2024 arXiv

  91. [99]

    Brink, P

    L. Brink, P. Di Vecchia, and P. S. Howe, Nucl. Phys. B 118, 76 (1977)

    1977

  92. [100]

    Brink, S

    L. Brink, S. Deser, B. Zumino, P. Di Vecchia, and P. S. Howe, Phys. Lett. B 64, 435 (1976), [Erratum: Phys.Lett.B 68, 488 (1977)]

    1976

  93. [101]

    Henneaux and C

    M. Henneaux and C. Teitelboim, Annals Phys. 143, 127 (1982)

    1982

  94. [102]

    Vines, D

    J. Vines, D. Kunst, J. Steinhoff, and T. Hinderer, Phys. Rev. D 93, 103008 (2016), [Erratum: Phys.Rev.D 104, 029902 (2021)], arXiv:1601.07529 [gr-qc]

    2016 arXiv

  95. [103]

    P. S. Howe, S. Penati, M. Pernici, and P. K. Townsend, Phys. Lett. B 215, 555 (1988)

    1988

  96. [104]

    Bastianelli, R

    F. Bastianelli, R. Bonezzi, O. Corradini, and E. La- tini, J. Phys. Conf. Ser. 1208, 012006 (2019), arXiv:1504.02683 [hep-th]

    2019 arXiv

  97. [105]

    Bastianelli, O

    F. Bastianelli, O. Corradini, and E. Latini, JHEP 02, 072, arXiv:hep-th/0701055

    arXiv

  98. [106]

    Bekaert, N

    X. Bekaert, N. Boulanger, and P. Sundell, Rev. Mod. Phys. 84, 987 (2012), arXiv:1007.0435 [hep-th]

    2012 arXiv

  99. [107]

    R. A. Porto, Phys. Rept. 633, 1 (2016), arXiv:1601.04914 [hep-th]

    2016 arXiv

  100. [108]

    Z. Liu, R. A. Porto, and Z. Yang, JHEP 06, 012, arXiv:2102.10059 [hep-th]

    arXiv

  101. [109]

    W. D. Goldberger, in Snowmass 2021 (2022) arXiv:2206.14249 [hep-th]

    2022 arXiv

  102. [110]

    Arkani-Hamed, T.-C

    N. Arkani-Hamed, T.-C. Huang, and Y.-t. Huang, JHEP 11, 070, arXiv:1709.04891 [hep-th]

    arXiv

  103. [111]

    Chung, Y.-T

    M.-Z. Chung, Y.-T. Huang, J.-W. Kim, and S. Lee, 9 JHEP 04, 156, arXiv:1812.08752 [hep-th]

    arXiv

  104. [112]

    Scheopner and J

    T. Scheopner and J. Vines, JHEP 12, 060, arXiv:2311.18421 [gr-qc]

    arXiv

  105. [113]

    Gambino, P

    C. Gambino, P. Pani, and F. Riccioni, Phys. Rev. D 109, 124018 (2024), arXiv:2403.16574 [hep-th]

    2024 arXiv

  106. [114]

    Cristofoli, P

    A. Cristofoli, P. H. Damgaard, P. Di Vecchia, and C. Heissenberg, JHEP 07, 122, arXiv:2003.10274 [hep- th]

    2003 arXiv

  107. [115]

    Bianchi, C

    M. Bianchi, C. Gambino, P. Pani, and F. Riccioni, Phys. Rev. D 111, 084013 (2025), arXiv:2412.01771 [gr-qc]

    2025 arXiv

  108. [116]

    Bianchi, C

    M. Bianchi, C. Gambino, F. Riccioni, and V. Zevola, (2025), arXiv:2505.04800 [hep-th]

    2025 arXiv

  109. [117]

    Marsat, Class

    S. Marsat, Class. Quant. Grav. 32, 085008 (2015), arXiv:1411.4118 [gr-qc]

    2015 arXiv

  110. [118]

    parameterized by theC1 coefficient multiplying the constants2. In generic d the Wilson coefficients are not fixed completely in the Kerr limit, but rather depend on a single unconstrained parameter D CES 2 =d2− 4 12 +Dd(d− 4)(d + 1), (16a) ˜CES 2 =d + 4 12 +d(d + 1)D, (16b) CB...

  111. [119]

    Steinhoff, Fund

    J. Steinhoff, Fund. Theor. Phys. 179, 615 (2015), arXiv:1412.3251 [gr-qc]

    2015 arXiv

  112. [120]

    Guevara, A

    A. Guevara, A. Ochirov, and J. Vines, Phys. Rev. D 100, 104024 (2019), arXiv:1906.10071 [hep-th]

    2019 arXiv

  113. [121]

    Haddad, Phys

    K. Haddad, Phys. Rev. D 105, 026004 (2022), arXiv:2109.04427 [hep-th]

    2022 arXiv

  114. [122]

    Aoude, K

    R. Aoude, K. Haddad, and A. Helset, JHEP 07, 072, arXiv:2203.06197 [hep-th]

    arXiv

  115. [123]

    Aoude, K

    R. Aoude, K. Haddad, and A. Helset, Phys. Rev. D 108, 024050 (2023), arXiv:2304.13740 [hep-th]

    2023 arXiv

  116. [124]

    Cangemi, M

    L. Cangemi, M. Chiodaroli, H. Johansson, A. Ochi- rov, P. Pichini, and E. Skvortsov, Phys. Rev. Lett. 131, 221401 (2023), arXiv:2212.06120 [hep-th]

    2023 arXiv

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