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Notes on the scattering amplitude / Wilson loop duality

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arxiv 1010.1167 v1 pith:NTQFTDG4 submitted 2010-10-06 hep-th

Simon Caron-Huot This is my paper · ORCID
classification hep-th
keywords loopdualityamplitudestheorywilsoncertainextensionlevel
verification ladder T0 review T1 audit T2 compute T3 formal
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We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We extend the duality to amplitudes with arbitrary helicity states by introducing a suitable supersymmetric extension of the Wilson loop. We show that this object is determined by a host of recursion relations, which are valid at tree level and at loop level for a certain "loop integrand" defined within the Lagrangian insertion procedure. These recursion relations reproduce the BCFW ones obeyed by tree-level scattering amplitudes, as well as their extension to loop integrands which appeared recently in the literature, establishing the duality to all orders in perturbation theory. Finally, we propose that a certain set of finite correlation functions can be used to compute all first derivatives of the logarithm of MHV amplitudes.

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Cited by 7 Pith papers

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

  1. QCD Scattering Amplitudes and Prescriptive Unitarity

    hep-th 2026-02 conditional novelty 7.0 of 10

    The maximally-transcendental part of planar two-loop six-gluon MHV QCD amplitudes is bootstrapped at symbol level and expressed in a 137-letter alphabet.

  2. Loops and legs: ABJM amplitudes from $f$-graphs

    hep-th 2026-01 unverdicted novelty 7.0 of 10

    ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes encoded in a permutation-symmetric generating function of planar f-graphs.

  3. Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons

    hep-th 2025-12 conditional novelty 7.0 of 10

    A general two-loop formula is obtained for all n-point 10d null polygon correlators in planar N=4 SYM, expressed in a conformal-integral basis and verified numerically at 11 points.

  4. Double spacelike collinear limits from multi-Regge kinematics

    hep-th 2025-07 conditional novelty 7.0 of 10

    The double spacelike collinear limit of planar N=4 SYM is governed by a generalized splitting amplitude that equals the six-point BDS-subtracted amplitude in multi-Regge kinematics.

  5. Two-loop MHV Form Factors from the Periodic Wilson Loop

    hep-th 2024-12 conditional novelty 7.0 of 10

    The periodic Wilson loop duality is extended beyond one loop, yielding the two-loop n-particle MHV form factor integrand and new five- and six-particle symbols.

  6. Generalized Wilson lines and the gravitational scattering of spinning bodies

    hep-th 2024-12 conditional novelty 7.0 of 10

    A new generalized Wilson line representation for spin-1/2 and classical spinning bodies is derived, reproducing known 2PM gravitational scattering observables.

  7. Soft Algebra for ${\cal N}=4$ SYM

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.

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