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

Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling zeta in a generalized Wilson loop operator of the N = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for zeta has fixed points at zeta = +/- 1 and zeta = 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 zeta at each order in 't Hooft coupling lambda) 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.

Automated summary

In this study, we extend previous work and find the two-loop term in the beta-function for the scalar coupling in a generalized Wilson loop operator of the N = 4 SYM theory. We also predict the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. Additionally, we compute the two-point correlators of scalars inserted on the Wilson line.