Concavity of the $Q\bar Q$ potential in ${\cal N}=4$ super Yang-Mills gauge theory and AdS/CFT duality

TL;DR

This paper derives a generalized concavity condition for static potentials in gauge theories with scalars and explores its use as a consistency check for the AdS/CFT duality, providing new insights into the potential's behavior.

Contribution

It introduces a novel concavity condition involving spatial and internal space derivatives for potentials from Wilson loops, and applies it to test the AdS/CFT correspondence.

Findings

Derived a generalized concavity condition for gauge theory potentials.

Proposed the condition as a nontrivial consistency check for AdS/CFT.

Discussed implications for the behavior of static potentials.

Abstract

We derive a generalised concavity condition for potentials between static sources obtained from Wilson loops coupling both to gauge bosons and a set of scalar fields. It involves the second derivatives with respect to the distance in ordinary space as well as with respect to the relative orientation in internal space. In addition we discuss the use of this field theoretical condition as a nontrivial consistency check of the AdS/CFT duality.