Higher order RG flow on the Wilson line in $$ \mathcal{N} $$ = 4 SYM

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