I would like to know, what are the simplest/starting/basic examples that are typically used to introduce students to how AdS/CFT really works? (not the MAGOO paper, as I am not sure it has concrete examples that a beginning student can work through)
For example, are the PhD. papers of Maldacena used for this purpose? What about the papers on holographic entanglement entropy (like the ones by Faulkner and Hartman and Shinsei Ryyu and Takayanagi)? Or the papers on worldsheet derivation of the duality like http://arxiv.org/abs/hep-th/0703141 (and its predecessors) and http://arxiv.org/abs/hep-th/0205297 and the Gopakumar-Vafa papers of '98?
Best Answer
One review I found helpful relates Type IIB superstrings on a maximally supersymmetric plane wave background to N=4 SYM:
Lectures on the Plane–Wave String/Gauge Theory Duality by Jan Christoph Plefka
It might be more conversational than what you're looking for, but this review by Polchinski has some great discussion and probably deserves the mention:
Introduction to Gauge/Gravity Duality by Joseph Polchinski
One very good, specific set of lecture notes already mentioned but deserving repeat is:
Supersymmetric Gauge Theories and the AdS/CFT Correspondence by Eric D'Hoker, Daniel Z. Freedman