On anomalous conformal Ward identities for Wilson loops on polygon-like contours with circular edges

Abstract

Abstract We derive the anomalous conformal Ward identities for $$ \mathcal{N} $$ N = 4 SYM Wilson loops on polygon-like contours with edges formed by circular arcs. With a suitable choice of parameterisation they are very similarly to those for local correlation functions. Their solutions have a conformally covariant factor depending on the distances of the corners times a conformally invariant remainder factor depending, besides on cross ratios of the corners, on the cusp angles and angles parameterising the torsion of the contours.