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

Abstract

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling <jats:italic>ζ</jats:italic> in a generalized Wilson loop operator of the <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for <jats:italic>ζ</jats:italic> has fixed points at <jats:italic>ζ</jats:italic> = ±1 and <jats:italic>ζ</jats:italic> = 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 <jats:italic>ζ</jats:italic> at each order in ‘t Hooft coupling <jats:italic>λ</jats:italic>) 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.</jats:p>