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

• Published in: The journal of high energy physics 2022-01, Vol.2022 (1)
• Main Authors: Beccaria, M., Giombi, S., Tseytlin, A. A.
• Format: Article
• Language: English
• Subjects: Approximation; Classical and Quantum Gravitation; Correlators; Coupling; Elementary Particles; Fixed points (mathematics); High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; String Theory; Symmetry
• ISSN: 1029-8479
• DOI: 10.1007/JHEP01(2022)056

A bstract 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.