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  • Letter
  • Open Access

Three-loop pentagonal Wilson loop with Lagrangian insertion

Dmitry Chicherin1,*, Johannes Henn2,†, Yongqun Xu3,‡, Shun-Qing Zhang2,§, and Yang Zhang3,4,5,∥

  • *Contact author: chicherin@lapth.cnrs.fr
  • †Contact author: henn@mpp.mpg.de
  • ‡Contact author: yongqunxu@mail.ustc.edu.cn
  • §Contact author: sqzhang@mpp.mpg.de
  • ∥Contact author: yzhphy@ustc.edu.cn
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Phys. Rev. D 114, L081905 – Published 13 October, 2026

DOI: https://doi.org/10.1103/19y3-r4tj

Abstract

Employing a cutting-edge bootstrap method, we analytically compute the three-loop pentagonal Wilson loop with Lagrangian insertion in planar N=4 super-Yang-Mills theory. Via a conjectured duality, this provides the first prediction for the maximally transcendental part of the four-loop five-point all-plus amplitude in pure Yang-Mills theory. Our starting point is an ansatz that encodes the known leading singularities of this object, as well as the relevant function space. The latter has become available only recently, thanks to an analytic computation of all three-loop five-point planar massless Feynman integrals. We determine the coefficients in the ansatz by imposing physical constraints. This includes a near-collinear expansion, which so far has not been applied to this quantity. Taken together, the constraints allow us to uniquely determine the symbol of the answer. We verify the symbol result by an independent integral reduction calculation, which moreover yields the full function-level answer.

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Outline

Information

Phys. Rev. D 114, L081905– Published 13 October, 2026
  • Received 30 March 2026
  • Accepted 17 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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