Concavity of the Q(Q)over-bar potential in N=4 super Yang-Mills gauge theory and AdS/CFT duality

We derive a generalised concavity condition for potentials between static s ources obtained from Wilson loops coupling both to gauge bosons and a set o f scalar fields. It involves the second derivatives with respect to the dis tance in ordinary space as well as with respect to the relative orientation in internal space. In addition we discuss the use of this field theoretica l condition as a nontrivial consistency check of the AdS/CFT duality. (C) 1 999 Elsevier Science B.V. All rights reserved.