Wilson loops at strong coupling for curved contours with cusps

TL;DR

This paper constructs minimal surfaces in AdS space for curved Wilson loop contours with cusps in N=4 SYM at strong coupling, calculates their regularized areas, and proves cusp anomalous dimensions depend only on cusp angles.

Contribution

It provides a new construction of minimal surfaces for curved, cusped Wilson loops and proves the cusp anomalous dimension's dependence solely on cusp angles.

Findings

Regularized area including divergences and finite parts computed.

Cusp anomalous dimensions depend only on cusp angles.

Minimal surfaces constructed for contours of intersecting circles.

Abstract

We construct the minimal surface in AdS, relevant for the strong coupling behaviour of local supersymmetric Wilson loops in N=4 SYM for a closed contour formed out of segments of two intersecting circles. Its regularised area is calculated including all divergent parts and the finite renormalised term. Furthermore we prove, that for generic planar curved contours with cusps the cusp anomalous dimensions are functions of the respective cusp angles alone. They do not depend on other local data of the cusps.