When Is Holography Consistent?

Understand

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.