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 recognized; and the question arises as to the circumstances under which it, and its Lorentzian counterpart, is satisfied. We discuss the fact that there are physically interesting situations in which one or both versions might, in principle, 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.