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

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.