Wilson loops for triangular contours with circular edges

TL;DR

This paper computes Wilson loops for triangular contours with circular edges in perturbation theory, revealing their conformal structure and dependence on geometric angles, with implications across different dimensions.

Contribution

It provides explicit calculations of Wilson loops for circular-edged triangles and analyzes their conformal properties and angle dependencies in various dimensions.

Findings

Wilson loops depend on cusp and torsion angles

Results align with anomalous conformal Ward identity

Analysis includes 3D and 2D cases

Abstract

We calculate Wilson loops in lowest order of perturbation theory for triangular contours whose edges are circular arcs. Based on a suitable disentanglement of the relations between metrical and conformal parameters of the contours, the result fits perfectly in the structure predicted by the anomalous conformal Ward identity. The conformal remainder function depends in the generic 4D case on three cusp and on three torsion angles. The restrictions on these angles imposed by the closing of the contour are discussed in detail and also for cases in 3D and 2D.