Loop equation and exact soft anomalous dimension in N = 4 super Yang-Mills

Simone Giombi, Shota Komatsu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


BPS Wilson loops in supersymmetric gauge theories have been the subjects of active research since they are often amenable to exact computation. So far most of the studies have focused on loops that do not intersect. In this paper, we derive exact results for intersecting 1/8 BPS Wilson loops in N = 4 supersymmetric Yang-Mills theory, using a combination of supersymmetric localization and the loop equation in 2d gauge theory. The result is given by a novel matrix-model-like representation which couples multiple contour integrals and a Gaussian matrix model. We evaluate the integral at large N , and make contact with the string worldsheet description at strong coupling. As an application of our results, we compute exactly a small-angle limit (and more generally near-BPS limits) of the cross anomalous dimension which governs the UV divergence of intersecting Wilson lines. The same quantity describes the soft anomalous dimension of scattering amplitudes of W -bosons in the Coulomb branch.

Original languageEnglish (US)
Article number75
JournalJournal of High Energy Physics
Issue number6
StatePublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • AdS-CFT Correspondence
  • Supersymmetric Gauge Theory
  • Wilson
  • ’t Hooft and Polyakov loops


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