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1. Dec 30, 2015

I believe I've read that null geodesics can reach the boundary of AdS space within finite affine parameter and that this allows for a causal connection between the bulk AdS spacetime and the boundary on which the CFT lives and that this is very important for AdS/CFT.

I can't find a reference for this just now so I was hoping that someone could either confirm that it's correct and explain why such a causal connection is needed for AdS/CFT or to tell me it's wrong and explain why no such causal connection can exist?

Thank you very much.

2. Jan 4, 2016

### Ravi Mohan

That is probably true. According to Nastase http://arxiv.org/abs/0712.0689 (in the book version https://www.amazon.com/Introduction-AdS-Correspondence-Hora-stase/dp/1107085853)
I am currently surveying http://arxiv.org/pdf/1204.1698v2.pdf and report back if I find some explanation for this statement.

3. Jan 6, 2016

### Ravi Mohan

Ok I am nearly finished with the article and my understanding regarding this subject is as follows:
In the above diagram, the region $\mathcal{A}$ (red color) is at the boundary of an $AdS$ space. By implementing the causal structure, one can draw the surfaces causally connected to $\mathcal{A}$ (for detailed prescription read section 2 of the article ). Now the surface $\Xi$ (which is again causally connected to $\mathcal{A}$) is of particular interest. In some cases (maximal symmetry at the boundary) it coincides with the co-dimension 2 surface in the bulk which gives the holographic entanglement entropy of $\mathcal{A}$ (the Ryu and Takayanagi proposal). In general the authors have shown that the surface $\Xi$ gives an upper bound to the entanglement entropy at the boundary.

I think this is only part of the answer, but one can acknowledge the role of causal connection for the AdS/CFT correspondence. I will post the complete answer when I have better understanding of the subject.