The moniker ADS/CFT is a class of theories and often its pretty broad when utilized by physicists. When people aren't being specific, it means roughly conformal field theory and gravity dual. So nowdays you have all sorts of crazy promising conjectures floating around. Like CFT/DS and CFT/Kerr-Newman etc. A pretty long list!
Then theres all the old dualities (N vs 1/N), weak-strong, Electro-Magnetic dualities, etc etc
Can anybody explain if this class of dualities can solve the problem that string theory depends on the choice of some background metric? Can AdS/CFT or any related duality "generate" a dynamical background?
I would say NO because AdS IS a specific background!
This question keeps coming up and has been thoroughly discussed before in many threads going back about 7 years now. The punchline is it depends exactly what you mean when you refine the question into actual math.
On one hand there is nothing (modulo a caveat, see below) intrinsically fixed about ADS/CFT. Everything is dynamical in the gravitational side, eg the bulk itself is completely dictated by general relativity and the space is free to move and change. You can add matter and watch things curve and fluctuate in complicated ways and so forth, blackholes arise and vanish etc etc. Meanwhile the CFT is fixed on some n-1 dimensional space although it can be defined nonperturbatively. So in a sense, using rather imprecise language, you have a dual between a background dependant formulation and a background independant one.
The one thing that does remain fixed on the gravtitational side is the choice of boundary conditions (or to be technically more correct, the superselection sector), but this is true in classical GR as well. For instance in a spacetime that is asymptotically ADS, you cannot force it to become flat (it takes an infinite amount of energy).
1. AdS/CFT makes a prediction for some quantities c’/c and k’/k, eqn (5).
2. This prediction is compared to the exactly known values for the 3D O(n) model at n = infinity, eqns (28) and (30).
3. The values disagree. Perhaps not by so much, but they are not exactly right.
The standare way of saying this is that the d-dimensional O(n) model does not have a classical gravitational dual, at least not in some neighborhood of n = infinity, d = 3, and hence not for generic n and d. There might be exceptional cases where a gravitational dual exist, e.g. the line d = 2, but generically it seems disproven by the above result. Also note that the O(n) model is one of the most important statphys models, which include the Ising, XY and Heisenberg models for n = 1, 2, 3.
I am on record of being skeptical about the physical relevance of AdS/CFT, but that was mainly because the premises do not seem to hold in nature: physical gravity lives in dS rather than AdS space, and physical QCD is asymptotically free rather than conformal. But the O(n) model at criticality is conformal, so the premises are satisfied, but the result is still wrong. If AdS/CFT does not apply to a CFT with infinitely many components or colors, when can it be trusted? And how do we know if it applies, if we don't have an exact solution to compare to?
An important aspect about the AdS/CFT is that it can be regarded as a classical/quantum dualism.
In this description, quantum phenomena such as the spontaneous breaking
of the center of the gauge group, magnetic confinement, and the mass gap are coded in
classical geometry. E. Witten hep-th/9803131
In AdS/QCD classical configuration of the fields in the AdS metric can reproduce non-perturbative QCD and the quantum running of the strong coupling constant.
This neglected aspect of AdS/CFT has been interpreted as coming from a deterministic theory, that is a fundamental classical field theory which effectively reproduces QM.