so my rough understanding is that the AdS/CFT duality is some sort of isomorphism between an N dimensional gravitational theory and a N-1 dimensional conformal field theory on the boundary.

The boundary of our 3+1D spacetime is the union of the cosmological horizon plus the event or apparent horizons of black holes in it, which are 2+1D spaces

So my question is: does this imply that there are some conformal fields evolving in those 2+1D physical boundaries at this very moment, that map one-on-one the evolution of the 3+1D spacetime? like some sort of crystal ball?

can you influence what happens in the 3+1D space by affecting what happens in those 2+1D boundaries?

I intentionally made this question as wild as possible so we mere non-stringy mortals can know where we stand with all this duality business

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    $\begingroup$ Just one small point: the holographic principle is actually based on general arguments using black hole thermodynamics and quantum mechanics. In that sense it should be a property of any consistent theory of quantum gravity and not necessarily only string theory. $\endgroup$ – Heidar Aug 24 '12 at 22:22

The answer is no, not from AdS/CFT, but yes from the holographic principle which gives rise to AdS/CFT, and which AdS/CFT confirms. The reason is the "C" in "CFT", the conformal symmetry is the special property of extremal black holes, that their horizons are in curved space. The cosmological horizon is locally flat space, every near horizon geometry is Rindler. The relation between the degrees of freedom of locally flat horizons and the space nearby and inside is not worked out at all, there are no examples of real thermal black hole boundary correspondence. What you do have are states corresponding to black holes in AdS space, but the description is now on the AdS boundary, not on the black hole boundary. Further, if you have two descriptions of the same small-size black hole in two different AdS spaces, they can't be matched up in any known way. So the description of AdS/CFT is only a shadow of full holographic principle, which does suggest something exactly like what you describe in the question.


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