Remarks on Holographic Wilson Loops and the Schwinger Effect

We extend Douglas' solution of the problem of finding minimal surfaces to anti-de Sitter space. The case of a circle as a boundary contour is elaborated. We discuss applications to ${\cal N}=4$ super Yang-Mills: a circular Wilson loop and the Schwinger process, where we calculate the $1/\sqrt{\lambda}$ correction to the critical value of constant electric field.