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

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.

Comments: Improved derivation of the basic inequalities including separation in rigorous and conjectured statements. No change concerning potentials derived via AdS/CFT