Wilson Loops and Integrability

TL;DR

This paper explores the integrability properties of Wilson loops in N=4 supersymmetric Yang-Mills theory, emphasizing non-local symmetries and minimal surface integrability at strong coupling, with some exact results discussed.

Contribution

It provides an introduction to Wilson loops' integrability, highlighting non-local symmetries and their relation to minimal surface problems at strong coupling.

Findings

Exact results for circular Wilson loop and cusp anomalous dimension

Identification of non-local symmetries in Wilson loops

Connection between integrability and minimal surface solutions

Abstract

These notes provide an introduction toward Wilson loops in N=4 supersymmetric Yang-Mills theory with a focus toward their integrability properties. In addition to a brief discussion of exact results for the circular Wilson loop and the cusp anomalous dimension, the notes focus on non-local symmetries, utilizing the integrability of the minimal surface problem that appears at strong coupling. This work is based on lectures given at the Young Researchers Integrability School and Workshop 2018. To appear in a special issue of J. Phys. A.