  Holographic duality relates two radically different kinds of theory: one with
gravity, one without. The very existence of such an equivalence imposes strong
consistency conditions which are, in the nature of the case, hard to satisfy.
Recently a particularly deep condition of this kind, relating the minimum of a
probe brane action to a gravitational bulk action (in a Euclidean formulation),
has been recognised; and the question arises as to the circumstances under
which it, and its Lorentzian counterpart, are satisfied. We discuss the fact
that there are physically interesting situations in which one or both versions
might, in principle, \emph{not} be satisfied. These arise in two distinct
circumstances: first, when the bulk is not an Einstein manifold, and, second,
in the presence of angular momentum. Focusing on the application of holography
to the quark-gluon plasma (of the various forms arising in the early Universe
and in heavy-ion collisions), we find that these potential violations never
actually occur. This suggests that the consistency condition is a "law of
physics" expressing a particular aspect of holography.
