Wilson loops on the Coulomb branch of $N=4$ super-Yang-Mills

TL;DR

This paper analyzes Wilson loops on the Coulomb branch of N=4 super-Yang-Mills by studying minimal surfaces in AdS space, revealing phase transitions and exact results.

Contribution

It provides a detailed phase diagram of Wilson loops on the Coulomb branch and suggests the straight line expectation value is tree-level exact.

Findings

Identified the Gross-Ooguri transition for circular loops.

Mapped the phase diagram of Wilson loops with respect to radius and separation.

Provided evidence for the exactness of the straight line expectation value.

Abstract

We study Wilson loops on the Coulomb branch of $N = 4$ super-Yang-Mills theory, by solving for minimal surfaces that connect the contour on the boundary with the D3-brane in the bulk of AdS$_5 \times S^5$. The circular loop undergoes the Gross-Ooguri transition as a function of the radius and angular separation, and we fully map its phase diagram. As a byproduct we find evidence that the expectation value of the straight line is tree-level exact.