# Can the study of the quantum information structure in QFT with holographic duals be relevant to string theory?

I'm interested in characterizing the behaviour of measures of quantum information in strongly correlated quantum field theories which admit a gravity dual description, e.g through AdS/CFT duality. In a more broad sense, my question points towards the following: in my limited experience, I use to accept that a duality means that we don't have any right to give a physical meaning to one part of the duality and use the other part as a mere computational tool. I would like to be illuminated by some experts.

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This is an interesting topic, and there may be a few things to be said. But, in the present form it is not clear to me what you are asking precisely. –  user566 Mar 4 '11 at 15:51
Thanks for your interest @Moshe R. I acknowledge that I wasn't very precise in my question. What I meant is the opposite to something like, what can AdS/CFT duality can tell us about condensed matter? My question should better be rephrased into: could the study of quantum entanglement in strongly coupled field theories (e.g-critical quantum many body systems-) with holographic duals tell us something interesting about string theory? –  xavimol Mar 4 '11 at 19:44

This is an interesting question, which quite a few people (myself included) find fascinating, and by and large still remains to be explored. To my knowledge, the farthest this idea has gotten so far is in the work of my colleague, Mark van Raamsdonk: Comments on quantum gravity and entanglement and the essay Building up spacetime with quantum entanglement which won the GRF essay competition last year. If you have background in many body systems and their description in terms of quantum information, your input on this set of issues could be valuable.

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Thanks again @Moshe. These two papers are really exciting. I hope to get more input on those issues soon. –  xavimol Mar 5 '11 at 9:36
I will also post something on this issue soon. –  xavimol Mar 5 '11 at 10:56

The holographic principle in general gives an equivalency between gravity in the interior of a space and the quantum fields on the boundary. So in the case of the $AdS_n$ its boundary $\partial AdS_n~\simeq~CFT_{n-1}$ is equivalent to a conformal field of one dimension lower. This is a form of the black hole holographic principle, where the field configuration of a black hole is defined by strings on the horizon. This means the number of pieces of information required to describe physics in dimensions $N$ is reduced to $N~-~1$ dimensional description.

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@Daniel Mods are not here to judge quality of an answer; if you think it is wrong, downvote and/or (better) add a comment explaining what is the problem. –  mbq Mar 7 '11 at 8:47