Remarks on Holographic Wilson Loops and the Schwinger Effect

TL;DR

This paper extends the minimal surface solution in anti-de Sitter space to analyze circular Wilson loops and the Schwinger effect in ${ m extbf{N}=4}$ super Yang-Mills, including quantum corrections to the critical electric field.

Contribution

It provides a generalized minimal surface solution for circular contours in AdS and applies it to compute quantum corrections in the Schwinger effect within super Yang-Mills theory.

Findings

Calculated the $1/\sqrt{\lambda}$ correction to the critical electric field.

Extended Douglas' minimal surface solution to AdS space.

Analyzed the Schwinger process using holographic Wilson loops.

Abstract

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.