Higher order RG flow on the Wilson line in N = 4 SYM

M. Beccaria, S. Giombi, A. A. Tseytlin

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10 Scopus citations


Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the N = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line.

Original languageEnglish (US)
Article number56
JournalJournal of High Energy Physics
Issue number1
StatePublished - Jan 2022

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • AdS-CFT Correspondence
  • Supersymmetry and Duality


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