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I am beginning to learn about the AdS/CFT correspondence, but I can't find a comprehensive introduction that includes the relevant gravitational/string theory physics. What specific areas of general relativity and superstring theory are essential for understanding the correspondence?

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Try here for background into the derivation of the AdS/CFT correspondence and also this thesis for an excellent introduction to the correspondance with regards to symmetry breaking.

Further to this, try these slides outlining the motivations and also providing a good reading list.

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I can recommend these lecture notes, which discuss many prerequisites for understanding the correspondence in a concise yet accessible way.

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