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I am about to begin my PhD in the applications of duality and holographic techniques to open problems in condensed matter physics. An area often called AdS/CMT. Having seen some relevant reviews, I realize that it is easy to find some nice descriptions and discussions concerning how holography is used to tackle such issues, i.e. holographic superconductors etc. However, in most such reviews the origin of the correspondence is only at best motivated, lacking any detailed discussion. I would like to ask your opinion about which two or three seminal papers regarding AdS/CFT should I focus on, in order to gain a deeper understanding on how the original correspondence was formulated on the first place. Brief remarks together with your suggestions are more than welcome.

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The following paper currently has almost 7500 citations. Why does it have so many? Because it is amazing; read it.

Anti de Sitter Space and Holography, by Edward Witten

The canonical, detailed review is the following paper which currently has nearly 4000 citations (pretty weak...I know).

Large N Field Theories, String Theory and Gravity, by MAGOO

Everyone I know who works in AdS/CFT has read Witten's paper above more than once, and at least once with pen and paper in hand to redo his computations. The paper by MAGOO is the go-to reference in the field.

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Concerning applications of holography, you should perhaps first read Andreas Karch's fresh introduction here:

http://motls.blogspot.com/2013/09/guest-blog-on-applications-of-holography.html?m=1

which also links to papers and proceedings that map the landscape of the papers, too. Josh is of course right that those are some of the key papers of AdS/CFT itself but you may have specifically wanted applications outside high-energy physics.

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