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AdS/CFT Question

  1. Dec 30, 2015 #1
    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. jcsd
  3. Jan 4, 2016 #2
    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.
     
  4. Jan 6, 2016 #3
    Causal.png
    Ok I am nearly finished with the article and my understanding regarding this subject is as follows:
    In the above diagram, the region [itex]\mathcal{A}[/itex] (red color) is at the boundary of an [itex]AdS[/itex] space. By implementing the causal structure, one can draw the surfaces causally connected to [itex]\mathcal{A}[/itex] (for detailed prescription read section 2 of the article ). Now the surface [itex]\Xi[/itex] (which is again causally connected to [itex]\mathcal{A}[/itex]) 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 [itex]\mathcal{A}[/itex] (the Ryu and Takayanagi proposal). In general the authors have shown that the surface [itex]\Xi[/itex] 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.
     
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