The notion of confinement in AdS/CFT In the frame of the AdS/CFT correspondence, how do I recognize in the SUGRA part that the dual field theory will exhibit confinement. I mean, can I see it in the metric? or should I compute a field to get this conclusion? Which field will provide the confinement information? The concept of confinement for the resulting theory will be the same as for a QCD-like theory?
 A: A not very rigorous answer to your question is that yes, the metric encodes information needed to determine if the theory is in a confined phase or not. If the spacetime is asymptotically locally AdS, or perhaps a variant thereof that would still be expected to be dual to a field theory (a good example is Klebanov-Strassler), then the test is to see if the radial, or holographic, direction has a minimum (excluding BH horizons). Well known examples of spacetimes obeying this criterion are AdS in global coordinates, where the minimum of the radial coordinate simply corresponds to the origin, or the AdS Soliton. I don't think Klebanov Witten is an example of a confined geometry--the metric is simply $AdS_5 \times T^{1,1}$, with the $AdS$ in Poincare coordinates.
As I said, this isn't a very rigorous answer. Basically if the spacetime "caps off" in the radial direction then it exhibits confinement. There's probably a way to make this concept well defined.
Not only is "capping off" not well defined, but also, the "capping off" is a property that strictly speaking, determines whether a theory has a mass gap or not. In other words, are there normalizable excitations of arbitrarily low energy (gapless) or not (gapped). It so happens that every example I know of a confined field theory state with a bulk dual also has a mass gap, but these are two logically distinct concepts. To determine if the bulk dual corresponds to a confined state, one diagnostic that does not rely on the mass gap is to find the free energy (Euclidean action) and to see how it scales with $N$. If it does not scale, then the solution is confined. This is exemplified in the Hawking-Page transition.
