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Double spacelike collinear limits from multi-Regge kinematics

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read In planar $\mathcal{N}=4$ super-Yang-Mills theory, the double spacelike collinear limit of two gluon pairs is governed by a universal generalised splitting amplitude that is exactly the six-point BDS-subtracted amplitude in multi-Regge…

desk verdict A strong letter with a genuinely new generalised splitting amplitude for double spacelike collinear limits, identified with the six-point MRK remainder; the N=6 core is solid, while the higher-point universality rests on symbol-level checks and remains a conjecture. read the letter →

arxiv 2507.05355 v1 pith:KLQFICQG submitted 2025-07-07 hep-th

Claude Duhr , Aniruddha Venkata , Chi Zhang This is my paper
classification hep-th
keywords doublespacelikecollinearlimitgeneralisedsplittingamplitudemulti-ReggekinematicsplanarN=4super-Yang-MillsBDSremainderfunctionBFKLeigenvaluefactorizationformfactors
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

In planar $\mathcal{N}=4$ super-Yang-Mills theory, when two adjacent pairs of gluons become collinear at the same time with both pairs in the spacelike region, the amplitude does not factorise into two independent splitting functions. Instead, the two collinear directions communicate through a generalised splitting amplitude. The paper shows that this generalised splitting amplitude is exactly the BDS-subtracted six-point amplitude in multi-Regge kinematics, after the appropriate analytic continuation. Since the multi-Regge remainder is governed by BFKL data known to all orders from integrability, the generalised splitting amplitude is fixed to all orders in the 't Hooft coupling. Explicit checks on amplitudes through eight particles and three loops, and on form factors through six particles and two loops, indicate that the same function controls every double spacelike collinear limit, so the result is universal.

What carries the argument

The object that carries the argument is the generalised splitting amplitude $\Delta_{I/II}(\tau,z)$, defined as the ratio of the full double-collinear splitting function to the product of two ordinary two-particle splitting amplitudes. Its two variables $z$ and $\bar z$ are the fixed ratios in Eq.~(13), and $\tau=\sqrt{u_1u_3}$, with the same $u_i$ as in the six-point case. The load-bearing identity is the duality between the double spacelike collinear limit and multi-Regge kinematics: after $u_2\to u_2 e^{2\pi i}$, the double-collinear limit $(u_1,u_2,u_3)\to(0,1,0)$ preserves exactly the combinations that define the MRK limit of $R_6$, so the universal correction can be read off from the Regge-cut contribution of the six-point BDS remainder. This turns the non-factorising collinear correlation into a Fourier-Mellin transform whose integrand is built from the cusp anomalous dimension, the adjoint BFKL eigenvalue and the regularised impact factor, and the same machinery yields all helicity components through the MHV and NMHV six-point remainders.

What would settle it

Evaluate the double spacelike collinear limit of the four-loop seven-point NMHV amplitude (or of a four-loop octagon) and compare the leading singular terms with the all-order expression in Eq.~(14); any term not expressible through $\Delta_{I/II}(\tau,z)$ with the $\tau,z$ fixed by Eq.~(13) would falsify the universality claim.

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Extended reading notes

Core claim

The central claim is that in the double spacelike collinear limit $p_1\parallel p_2$, $p_3\parallel p_4$, the amplitude obeys $A_N \sim \sum_{h,h'} \mathrm{Sp}^{(2)}_h \mathrm{Sp}^{(2)}_{h'} \Delta_{I/II}(\tau,z)\, A_{N-2}$, where $\Delta_{I/II}$ is a universal generalised splitting coefficient that keeps the two collinear clusters correlated. In region I, after continuing $u_2 \to u_2 e^{2\pi i}$ and taking $(u_1,u_2,u_3)\to(0,1,0)$ with the two ratios in Eq.~(13) held fixed, the configuration of conformal cross-ratios is identical to the multi-Regge limit of the six-point BDS-subtracted amplitude; region II is the corresponding $3\to 3$ continuation. Consequently $\Delta^{++}_I=\Delta^{--}_I=e^{i\delta_6}\mathcal{M}(R_6^{\mathrm{MHV}})$, and the mixed-helicity components are obtained from the NMHV six-point remainder in MRK with $z\leftrightarrow \bar z$, with the phase $e^{i\delta_6}$ coming from the BDS factor. The result is an explicit Fourier-Mellin representation built from the cusp anomalous dimension, the adjoint BFKL eigenvalue and a regularised impact factor, all of which are known to all orders from integrability, so the generalised splitting amplitude itself is fixed to all orders in the 't Hooft coupling. Explicit symbol computations for seven- and eight-point MHV and NMHV amplitudes through three loops and for MHV form factors through six points and two loops show the same $\Delta_{I/II}$ in every case, and the paper conjectures this universality for all double spacelike collinear limits in planar $\mathcal{N}=4$ SYM.

Load-bearing premise

The load-bearing premise is that the double collinear limit and the multi-Regge limit land on the same analytic branch of the six-point amplitude and that the three conformal cross-ratios capture all kinematic information; if a fourth variable or a different branch entered, the identification of the splitting amplitude with the Regge amplitude would fail.

Editorial extensions

If this is right

  • The generalised splitting amplitude can be evaluated to any loop order, because Eq.~(14) expresses it through the cusp anomalous dimension, the adjoint BFKL eigenvalue and the regularised impact factor, all of which are known from integrability.
  • Every double spacelike collinear limit in planar $\mathcal{N}=4$ SYM is governed by the same universal function, as verified for amplitudes up to eight particles and three loops and for form factors up to six particles and two loops.
  • Correlations between two spacelike collinear clusters occur at leading colour, so the proposed generalisation of collinear factorisation breaking is realised in a concrete gauge theory.
  • Known multi-Regge results for the six-point BDS remainder become boundary data for the collinear behaviour of higher-point amplitudes and form factors, feeding directly into bootstrap programmes.
  • The triviality of the remainder in Euclidean multi-Regge kinematics corresponds to the factorised timelike double-collinear limit, while the non-factorising spacelike limit is carried by the same Regge-cut contribution.

Reading between the lines

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

  • If the duality is exact, the same cross-ratio argument should extend the all-order result to double collinear limits of non-adjacent pairs or of more than two collinear pairs, although the paper only treats adjacent pairs explicitly.
  • The form-factor analysis reveals extra symmetric regions I' and II' related to I and II by $\xi_i\to 1-\xi_i$; testing whether analogous regions appear in amplitudes would provide a sharp check of universality.
  • The leading-colour correlation between collinear beams found here suggests that strictly factorised parton-distribution evolution could receive double-collinear corrections in observables that are not fully inclusive, and quantifying that effect is a direct phenomenological test.
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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

2 major / 4 minor

Summary. This paper studies the double spacelike collinear (DSL) limit of colour-ordered amplitudes and form factors in planar N=4 super Yang-Mills theory, in which two adjacent pairs of external particles become simultaneously collinear while the virtualities of both pairs are spacelike. The authors show that in this limit the amplitude does not factorise into a product of ordinary two-particle splitting amplitudes; instead, a generalised splitting amplitude Δ_{I/II}(τ,z) correlating the two collinear directions appears, confirming a proposal of Cieri, Dhani and Rodrigo. For N=6, they identify this function, after a specified analytic continuation and a boundary limit, with the BDS-subtracted six-point amplitude in multi-Regge kinematics, and they write Δ explicitly in terms of the BFKL eigenvalue and impact factor, Eq. (14), which is known to all orders from integrability. They further report symbol-level checks for seven- and eight-point MHV and NMHV amplitudes up to three loops and for form factors up to two and three loops, and they conjecture that Δ is universal.

Significance. The N=6 identification is the paper's main technical achievement; the cross-ratio argument in Section III A and the helicity analysis in Appendix B make the map between the DSL limit and MRK concrete and internally consistent. If the universality conjecture holds, the paper provides the first analytic all-orders expression for a generalised splitting amplitude in a gauge theory and establishes a non-trivial duality between a collinear limit and the multi-Regge limit that is directly testable by future fixed-order and bootstrap computations. The explicit formula (14) is falsifiable, and the authors are appropriately cautious in presenting the higher-point universality as a conjecture rather than a theorem. The main weakness is that the higher-point and form-factor evidence is reported only at symbol level and is not shown in the letter, which limits the strength of the universality claim.

major comments (2)
  1. [Section III B] The universality evidence for N=7, N=8 and for form factors is based on symbols only, as the text states that the seven- and eight-point checks were performed 'for the symbols' and no function-level results are shown. Because a symbol is insensitive to the Riemann-sheet choice, to the phase e^{±iδ6} in Eq. (10), and to transcendental constants, these checks do not by themselves establish that the higher-point DSL limit is exactly the same function M(R6) on the same sheet as in Eq. (14). This is a load-bearing point for the abstract's statement that 'the same function governs' all these quantities. I recommend either showing at least one explicit function-level check for a higher-point amplitude or a form factor, or explaining which additional analytic-continuation data fix the branch, or explicitly limiting the universality claim to a symbol-level conjecture.
  2. [Section III B, Eq. (10)] The letter notes that for N=7 there are multiple physical regions compatible with the DSL conditions (8) and (9), and says that analytic continuation to 'various compatible regions' was performed, but it does not report the region-dependent signs or the ξ_i→1−ξ_i cases mentioned for form factors. If different compatible regions select different Riemann sheets, the sign and phase choices in Eq. (10) could change, and the statement that Δ_{I/II} is universal would be incomplete. Please provide a table or appendix listing the regions checked for each N and form factor, together with the corresponding signs of Δ_{I/II} and the values of τ and z used.
minor comments (4)
  1. [Section III A, Eq. (13)] Please state explicitly that the limit in Eq. (13) is taken after the analytic continuation u2→u2 e^{2πi} and that the path approaches the boundary u2→1 with u1,u3→0 at the specified rates; this will prevent misreading the endpoint condition alone as the full identification.
  2. [Section II] The sentence 'RN is unity or an R-invariant for N≤5' uses the term R-invariant before it is introduced; either define it there or move the definition earlier.
  3. [Appendix B, Eqs. (B3)–(B4)] The notation RMHV6 is used both for the BDS-subtracted ratio AMHV6/(ABDS6 Atree_MHV) and for its double-collinear-limit or MRK value; please use different symbols for the function and for its limits.
  4. [Section III B] The phrase 'with p6 replaced by pN' is slightly ambiguous for N=7 and N=8; clarify that τ and z are defined by the same cross-ratios with the leg labelled 6 relabelled as N.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DSL/MRK identification equates two limits of the same BDS-subtracted function, and no equation reduces to its input by construction.

full rationale

The derivation chain is self-contained against external benchmarks. In Sec. III A the paper defines the generalised splitting amplitude through the factorisation ansatz (B2) and then identifies its six-point value with the MRK limit of R6 via the cross-ratio statement (13): after the analytic continuation (11), both the double spacelike collinear limit and the multi-Regge limit drive (u1,u2,u3) to (0,1,0) with the same finite ratios. This is an equality of two limits of the same dual-conformally-invariant function, not a definition of Δ in terms of M(R6) or a fitted parameter relabelled as a prediction. The all-orders expression (14) imports the BFKL eigenvalue, impact factor and cusp anomalous dimension from prior published work ([25,41,42,46,49,50,51]); refs [46,49,50] include a present author, but they are fixed-order/all-order MRK computations independent of the DSL factorisation, so citing them is legitimate evidence rather than a load-bearing self-citation loop. The universality checks in Sec. III B are admittedly symbol-level only ('we have performed explicit computations of the DSL collinear limits for the symbols of seven- and eight-point MHV and NMHV amplitudes up to 3 loops'), so the Riemann-sheet and phase content of the higher-point claim is less directly tested; this is a completeness/correctness limitation, not a circularity. No step in the paper reduces to its own input by construction.

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

The paper relies on well-established results from dual conformal symmetry and integrability, and introduces no new free parameters or invented entities. The main assumptions are the validity of the BDS ansatz and the identification of the two kinematic limits on the appropriate analytic branch.

assumptions (3)
  • domain assumption Planar N=4 SYM amplitudes factorize as Atree_MHV * ABDS_N * R_N (Eq. 5).
    This factorization from dual conformal symmetry underpins the definition of the BDS-subtracted remainder R_N used throughout.
  • domain assumption The six-point BDS-subtracted amplitude in multi-Regge kinematics is known to all orders from integrability (Basso, Caron-Huot, Sever).
    The all-orders statement for the generalized splitting amplitude inherits this external result (Ref. [25]).
  • domain assumption The double collinear limit and the multi-Regge limit of R6 commute and the analytic continuation selects the unique relevant Riemann sheet.
    The identification of Delta with M(R6) in Eq. (14) relies on this premise, which is argued but not proven.

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Cite this review

Pith. "Pith review of Double spacelike collinear limits from multi-Regge kinematics." pith.science (2026). https://pith.science/paper/KLQFICQG

@misc{pith2026250705355,
  author       = {Pith},
  title        = {Pith review of: Double spacelike collinear limits from multi-Regge kinematics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KLQFICQG}},
  note         = {Machine review of arXiv:2507.05355}
}
abstract

We study scattering amplitudes and form factors in planar $\mathcal{N}=4$ Super Yang-Mills theory in the limit where two pairs of gluons become collinear. We find that, when the virtualities of both collinear pairs are spacelike, the collinear factorisation of the amplitude involves a generalised splitting amplitude that correlates the two collinear directions, confirming a recent proposal in the literature. Remarkably, we find that our generalised splitting amplitude agrees with the Bern-Dixon-Smirnov (BDS) subtracted six-point amplitude in multi-Regge kinematics. The latter can be explicitly evaluated using integrability to all orders in the coupling. We also present compelling evidence for the universality of the generalised splitting amplitude, by showing that the same function governs the double spacelike collinear limit of scattering amplitudes with up to 8 particles and 3 loops and form factors with up to 6 particles and 2 loops.

Figures

Figures reproduced from arXiv: 2507.05355 by the authors.

Figure 1
Figure 1. Timelike versus spacelike collinear factorisation [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

80 extracted references · 35 canonical work pages · cited by 4 Pith papers

  1. [17]

    Cieri, P

    L. Cieri, P. K. Dhani, and G. Rodrigo, Catani’s generalization of collinear factorization breaking , arXiv:2402.14749

    arXiv

  2. [1]

    V. N. Gribov and L. N. Lipatov, Deep inelastic e-p scattering in perturbation theory , Sov. J. Nucl. Phys. 15 (1972) 438–450

    work page 1972

  3. [2]

    Y. L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+– e− Annihilation by Perturbation Theory in Quantum Chromodynamics. , Sov. Phys. JETP 46 (1977) 641–653

    work page 1977

  4. [3]

    Altarelli and G

    G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298–318

    work page 1977

  5. [4]

    J. C. Collins, D. E. Soper, and G. F. Sterman, Soft Gluons and Factorization , Nucl. Phys. B 308 (1988) 833–856

    work page 1988

  6. [5]

    J. C. Collins, D. E. Soper, and G. F. Sterman, Factorization of Hard Processes in QCD , Adv. Ser. Direct. High Energy Phys. 5 (1989) 1–91, [hep-ph/0409313]

    arXiv 1989

  7. [6]

    Collins, Foundations of Perturbative QCD , vol

    J. Collins, Foundations of Perturbative QCD , vol. 32. Cambridge University Press, 2011

    work page 2011

  8. [7]

    S. B. Libby and G. F. Sterman, Jet and Lepton Pair Production in High-Energy Lepton-Hadron and Hadron-Hadron Scattering, Phys. Rev. D 18 (1978) 3252

    work page 1978

Show all 80 references
  1. [8]

    D. A. Kosower, All order collinear behavior in gauge theories, Nucl. Phys. B 552 (1999) 319–336, [hep-ph/9901201]

    1999 arXiv

  2. [9]

    Feige and M

    I. Feige and M. D. Schwartz, Hard-Soft-Collinear Factorization to All Orders , Phys. Rev. D 90 (2014), no. 10 105020, [ arXiv:1403.6472]

    2014 arXiv

  3. [10]

    Catani, D

    S. Catani, D. de Florian, and G. Rodrigo, Space-like (versus time-like) collinear limits in QCD: Is factorization violated?, JHEP 07 (2012) 026, [arXiv:1112.4405]

    2012 arXiv

  4. [11]

    J. Henn, R. Ma, Y. Xu, K. Yan, Y. Zhang, and H. X. Zhu, Two-Loop Spacelike Splitting Amplitude for N=4 Super-Yang-Mills Theory, arXiv:2406.14604

    arXiv

  5. [12]

    X. Guan, F. Herzog, Y. Ma, B. Mistlberger, and A. Suresh, Splitting amplitudes at N 3LO in QCD , JHEP 01 (2025) 090, [ arXiv:2408.03019]

    2025 arXiv

  6. [13]

    Catani, D

    S. Catani, D. de Florian, and G. Rodrigo, The Triple collinear limit of one loop QCD amplitudes , Phys. Lett. B 586 (2004) 323–331, [ hep-ph/0312067]

    2004 arXiv

  7. [14]

    C. Duhr, T. Gehrmann, and M. Jaquier, Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N 3LO, JHEP 02 (2015) 077, [arXiv:1411.3587]

    2015 arXiv

  8. [15]

    Badger, F

    S. Badger, F. Buciuni, and T. Peraro, One-loop triple collinear splitting amplitudes in QCD , JHEP 09 (2015) 188, [arXiv:1507.05070]

    2015 arXiv

  9. [16]

    Czakon and S

    M. Czakon and S. Sapeta, Complete collection of one-loop triple-collinear splitting operators for dimensionally-regulated QCD, JHEP 07 (2022) 052, [arXiv:2204.11801]

    2022 arXiv

  10. [18]

    Caron-Huot, L

    S. Caron-Huot, L. J. Dixon, F. Dulat, M. von Hippel, A. J. McLeod, and G. Papathanasiou, Six-Gluon amplitudes in planar N = 4 super-Yang-Mills theory at six and seven loops , JHEP 08 (2019) 016, [arXiv:1903.10890]

    2019 arXiv

  11. [19]

    L. J. Dixon, J. Drummond, T. Harrington, A. J. McLeod, G. Papathanasiou, and M. Spradlin, Heptagons from the Steinmann Cluster Bootstrap , JHEP 02 (2017) 137, [ arXiv:1612.08976]

    2017 arXiv

  12. [20]

    Drummond, J

    J. Drummond, J. Foster, O. G¨ urdo˘ gan, and G. Papathanasiou, Cluster adjacency and the four-loop NMHV heptagon , JHEP 03 (2019) 087, [arXiv:1812.04640]

    2019 arXiv

  13. [21]

    Caron-Huot, Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills , JHEP 12 (2011) 066, [ arXiv:1105.5606]

    S. Caron-Huot, Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills , JHEP 12 (2011) 066, [ arXiv:1105.5606]

    2011 arXiv

  14. [22]

    S. He, Z. Li, and C. Zhang, Two-loop octagons, algebraic letters and ¯Q equations, Phys. Rev. D 101 (2020), no. 6 061701, [ arXiv:1911.01290]

    2020 arXiv

  15. [23]

    S. He, Z. Li, and C. Zhang, The symbol and alphabet of two-loop NMHV amplitudes from ¯Q equations, JHEP 03 (2021) 278, [ arXiv:2009.11471]

    2021 arXiv

  16. [24]

    Li and C

    Z. Li and C. Zhang, The three-loop MHV octagon from 7 Q equations, JHEP 12 (2021) 113, [ arXiv:2110.00350]

    2021 arXiv

  17. [25]

    Basso, S

    B. Basso, S. Caron-Huot, and A. Sever, Adjoint BFKL at finite coupling: a short-cut from the collinear limit , JHEP 01 (2015) 027, [ arXiv:1407.3766]

    2015 arXiv

  18. [26]

    Arkani-Hamed, L

    N. Arkani-Hamed, L. J. Dixon, A. J. McLeod, M. Spradlin, J. Trnka, and A. Volovich, Solving Scattering in N = 4 Super-Yang-Mills Theory , arXiv:2207.10636

    arXiv

  19. [27]

    J. M. Drummond, J. Henn, V. A. Smirnov, and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064, [ hep-th/0607160]

    2007 arXiv

  20. [28]

    J. M. Drummond, J. M. Henn, and J. Plefka, Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory, JHEP 05 (2009) 046, [arXiv:0902.2987]

    2009 arXiv

  21. [29]

    V. P. Nair, A Current Algebra for Some Gauge Theory Amplitudes, Phys. Lett. B 214 (1988) 215–218

    1988

  22. [30]

    Arkani-Hamed, F

    N. Arkani-Hamed, F. Cachazo, and J. Kaplan, What is the Simplest Quantum Field Theory? , JHEP 09 (2010) 016, [arXiv:0808.1446]

    2010 arXiv

  23. [31]

    J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory , Nucl. Phys. B 828 (2010) 317–374, [ arXiv:0807.1095]

    2010 arXiv

  24. [32]

    Z. Bern, L. J. Dixon, and V. A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond , Phys. Rev. D 72 (2005) 085001, [ hep-th/0505205]

    2005 arXiv

  25. [33]

    Z. Bern, L. J. Dixon, D. A. Kosower, R. Roiban, M. Spradlin, C. Vergu, and A. Volovich, The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev. D 78 (2008) 045007, [ arXiv:0803.1465]

    2008 arXiv

  26. [34]

    Spiering, M

    A. Spiering, M. Wilhelm, and C. Zhang, All Planar Two-Loop Amplitudes in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 134 (2025), no. 7 071602, [arXiv:2406.15549]

    2025 arXiv

  27. [35]

    L. J. Mason and D. Skinner, Dual Superconformal Invariance, Momentum Twistors and Grassmannians , JHEP 11 (2009) 045, [ arXiv:0909.0250]

    2009 arXiv

  28. [36]

    Anastasiou, Z

    C. Anastasiou, Z. Bern, L. J. Dixon, and D. A. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett. 91 (2003) 251602, [ hep-th/0309040]

    2003 arXiv

  29. [37]

    Caron-Huot, Notes on the scattering amplitude / Wilson loop duality , JHEP 07 (2011) 058, [arXiv:1010.1167]

    S. Caron-Huot, Notes on the scattering amplitude / Wilson loop duality , JHEP 07 (2011) 058, [arXiv:1010.1167]

    2011 arXiv

  30. [38]

    Basso, A

    B. Basso, A. Sever, and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for N=4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 111 (2013), no. 9 091602, [ arXiv:1303.1396]

    2013 arXiv

  31. [39]

    Bartels, L

    J. Bartels, L. N. Lipatov, and A. Sabio Vera, BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes, Phys. Rev. D 80 (2009) 045002, [arXiv:0802.2065]

    2009 arXiv

  32. [40]

    Bartels, L

    J. Bartels, L. N. Lipatov, and A. Sabio Vera, N=4 supersymmetric Yang Mills scattering amplitudes at high energies: The Regge cut contribution , Eur. Phys. J. C 65 (2010) 587–605, [ arXiv:0807.0894]

    2010 arXiv

  33. [41]

    L. N. Lipatov and A. Prygarin, BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills , Phys. Rev. D 83 (2011) 125001, [ arXiv:1011.2673]

    2011 arXiv

  34. [42]

    V. S. Fadin and L. N. Lipatov, BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N=4 SUSY , Phys. Lett. B 706 (2012) 470–476, [ arXiv:1111.0782]

    2012 arXiv

  35. [43]

    Caron-Huot, When does the gluon reggeize? , JHEP 05 (2015) 093, [ arXiv:1309.6521]

    S. Caron-Huot, When does the gluon reggeize? , JHEP 05 (2015) 093, [ arXiv:1309.6521]

    2015 arXiv

  36. [44]

    Lipatov, A

    L. Lipatov, A. Prygarin, and H. J. Schnitzer, The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory, JHEP 01 (2013) 068, [ arXiv:1205.0186]

    2013 arXiv

  37. [45]

    L. J. Dixon and M. von Hippel, Bootstrapping an NMHV amplitude through three loops , JHEP 10 (2014) 065, [arXiv:1408.1505]

    2014 arXiv

  38. [46]

    Del Duca, S

    V. Del Duca, S. Druc, J. Drummond, C. Duhr, F. Dulat, R. Marzucca, G. Papathanasiou, and B. Verbeek, The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy , JHEP 06 (2018) 116, [ arXiv:1801.10605]

    2018 arXiv

  39. [47]

    Bartels, L

    J. Bartels, L. N. Lipatov, and A. Prygarin, MHV amplitude for 3 →3 gluon scattering in Regge limit , Phys. Lett. B 705 (2011) 507–512, [ arXiv:1012.3178]

    2011 arXiv

  40. [48]

    Sen, Asymptotic Behavior of the Fermion and Gluon Exchange Amplitudes in Massive Quantum Electrodynamics in the Regge Limit , Phys

    A. Sen, Asymptotic Behavior of the Fermion and Gluon Exchange Amplitudes in Massive Quantum Electrodynamics in the Regge Limit , Phys. Rev. D 27 (1983) 2997

    1983

  41. [49]

    L. J. Dixon, C. Duhr, and J. Pennington, Single-valued harmonic polylogarithms and the multi-Regge limit , JHEP 10 (2012) 074, [ arXiv:1207.0186]

    2012 arXiv

  42. [50]

    L. J. Dixon, J. M. Drummond, C. Duhr, and J. Pennington, The four-loop remainder function and multi-Regge behavior at NNLLA in planar N = 4 super-Yang-Mills theory, JHEP 06 (2014) 116, [arXiv:1402.3300]

    2014 arXiv

  43. [51]

    Beisert, B

    N. Beisert, B. Eden, and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021, [ hep-th/0610251]

    2007 arXiv

  44. [52]

    Remiddi and J

    E. Remiddi and J. A. M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725–754, [hep-ph/9905237]

    2000 arXiv

  45. [53]

    F. C. Brown, Single-valued multiple polylogarithms in one variable , C. R. Acad. Sci. Paris, Ser. I 338 (2004) 527

    2004

  46. [54]

    F. C. Brown, Single-valued hyperlogarithms and unipotent differential equations, 2004

    2004

  47. [55]

    J. M. Drummond, G. Papathanasiou, and M. Spradlin, A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon , JHEP 03 (2015) 072, [arXiv:1412.3763]

    2015 arXiv

  48. [56]

    L. J. Dixon, O. G¨ urdo˘ gan, Y.-T. Liu, A. J. McLeod, and M. Wilhelm, Antipodal Self-Duality for a Four-Particle Form Factor, Phys. Rev. Lett. 130 (2023), no. 11 111601, [ arXiv:2212.02410]

    2023 arXiv

  49. [57]

    L. J. Dixon and S. Xin, A two-loop four-point form factor at function level , JHEP 01 (2025) 012, [arXiv:2411.01571]

    2025

  50. [58]

    Li, Two-loop MHV form factors from the periodic Wilson loop, JHEP 05 (2025) 209, [ arXiv:2412.17974]

    Z. Li, Two-loop MHV form factors from the periodic Wilson loop, JHEP 05 (2025) 209, [ arXiv:2412.17974]

    2025 arXiv

  51. [59]

    Pennington, The six-point remainder function to all loop orders in the multi-Regge limit , JHEP 01 (2013) 059, [arXiv:1209.5357]

    J. Pennington, The six-point remainder function to all loop orders in the multi-Regge limit , JHEP 01 (2013) 059, [arXiv:1209.5357]

    2013 arXiv

  52. [60]

    Broedel and M

    J. Broedel and M. Sprenger, Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space , JHEP 05 (2016) 055, [arXiv:1512.04963]

    2016 arXiv

  53. [61]

    Bartels, L

    J. Bartels, L. N. Lipatov, and A. Prygarin, Collinear and Regge behavior of 2 - > 4 MHV amplitude in N = 4 super Yang-Mills theory, arXiv:1104.4709. 8

    arXiv

  54. [62]

    Bartels, A

    J. Bartels, A. Kormilitzin, L. N. Lipatov, and A. Prygarin, BFKL approach and 2 → 5 maximally helicity violating amplitude in N = 4 super-Yang-Mills theory, Phys. Rev. D 86 (2012) 065026, [arXiv:1112.6366]

    2012 arXiv

  55. [63]

    L. N. Lipatov and A. Prygarin, Mandelstam cuts and light-like Wilson loops in N=4 SUSY , Phys. Rev. D 83 (2011) 045020, [ arXiv:1008.1016]

    2011 arXiv

  56. [64]

    Prygarin, M

    A. Prygarin, M. Spradlin, C. Vergu, and A. Volovich, All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology, Phys. Rev. D 85 (2012) 085019, [ arXiv:1112.6365]

    2012 arXiv

  57. [65]

    Bartels, V

    J. Bartels, V. Schomerus, and M. Sprenger, Multi-Regge Limit of the n-Gluon Bubble Ansatz , JHEP 11 (2012) 145, [arXiv:1207.4204]

    2012 arXiv

  58. [66]

    Bartels, A

    J. Bartels, A. Kormilitzin, and L. Lipatov, Analytic structure of the n = 7 scattering amplitude in N = 4 SYM theory in the multi-Regge kinematics: Conformal Regge pole contribution, Phys. Rev. D 89 (2014), no. 6 065002, [arXiv:1311.2061]

    2014 arXiv

  59. [67]

    Bartels, A

    J. Bartels, A. Kormilitzin, and L. N. Lipatov, Analytic structure of the n = 7 scattering amplitude in N = 4 theory in multi-Regge kinematics: Conformal Regge cut contribution, Phys. Rev. D 91 (2015), no. 4 045005, [arXiv:1411.2294]

    2015 arXiv

  60. [68]

    Bartels, V

    J. Bartels, V. Schomerus, and M. Sprenger, Heptagon Amplitude in the Multi-Regge Regime , JHEP 10 (2014) 067, [arXiv:1405.3658]

    2014 arXiv

  61. [69]

    Bartels, V

    J. Bartels, V. Schomerus, and M. Sprenger, The Bethe roots of Regge cuts in strongly coupled N = 4 SYM theory, JHEP 07 (2015) 098, [ arXiv:1411.2594]

    2015 arXiv

  62. [70]

    Bargheer, G

    T. Bargheer, G. Papathanasiou, and V. Schomerus, The Two-Loop Symbol of all Multi-Regge Regions , JHEP 05 (2016) 012, [ arXiv:1512.07620]

    2016 arXiv

  63. [71]

    Broedel, M

    J. Broedel, M. Sprenger, and A. Torres Orjuela, Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge kinematics, Nucl. Phys. B 915 (2017) 394–413, [arXiv:1606.08411]

    2017 arXiv

  64. [72]

    Bargheer, Systematics of the Multi-Regge Three-Loop Symbol, JHEP 11 (2017) 077, [ arXiv:1606.07640]

    T. Bargheer, Systematics of the Multi-Regge Three-Loop Symbol, JHEP 11 (2017) 077, [ arXiv:1606.07640]

    2017 arXiv

  65. [73]

    Del Duca, S

    V. Del Duca, S. Druc, J. Drummond, C. Duhr, F. Dulat, R. Marzucca, G. Papathanasiou, and B. Verbeek, Multi-Regge kinematics and the moduli space of Riemann spheres with marked points , JHEP 08 (2016) 152, [ arXiv:1606.08807]

    2016 arXiv

  66. [74]

    Marzucca and B

    R. Marzucca and B. Verbeek, The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy, JHEP 07 (2019) 039, [arXiv:1811.10570]

    2019 arXiv

  67. [75]

    Del Duca, S

    V. Del Duca, S. Druc, J. M. Drummond, C. Duhr, F. Dulat, R. Marzucca, G. Papathanasiou, and B. Verbeek, All-order amplitudes at any multiplicity in the multi-Regge limit , Phys. Rev. Lett. 124 (2020), no. 16 161602, [ arXiv:1912.00188]

    2020 arXiv

  68. [76]

    Del Duca, C

    V. Del Duca, C. Duhr, F. Dulat, and B. Penante, All two-loop MHV remainder functions in multi-Regge kinematics, JHEP 01 (2019) 162, [ arXiv:1811.10398]

    2019 arXiv

  69. [77]

    Bargheer, V

    T. Bargheer, V. Chestnov, and V. Schomerus, The Multi-Regge Limit from the Wilson Loop OPE , JHEP 05 (2020) 002, [ arXiv:1906.00990]

    2020 arXiv

  70. [78]

    Bartels, Analytic structure of the 8-point scattering amplitude in multi-Regge kinematics in N =4 SYM : conformal Regge pole and Regge cut contributions , arXiv:2005.08818

    J. Bartels, Analytic structure of the 8-point scattering amplitude in multi-Regge kinematics in N =4 SYM : conformal Regge pole and Regge cut contributions , arXiv:2005.08818

    2005 arXiv

  71. [79]

    Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP 05 (2013) 135, [arXiv:0905.1473]

    A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP 05 (2013) 135, [arXiv:0905.1473]

    2013 arXiv

  72. [80]

    Basso and A

    B. Basso and A. G. Tumanov, Wilson loop duality and OPE for super form factors of half-BPS operators , JHEP 02 (2024) 022, [ arXiv:2308.08432]

    2024 arXiv

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