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AdS/CFT is a special case of the holographic principle. It states that a quantum gravitating theory in Anti-de-Sitter (AdS) space is exactly equivalent to the gauge theory/Conformal Field Theory (CFT) on its boundary.

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Condensed matter application of AdS/CFT

I'm going to be teaching a course on gauge/gravity duality (aka AdS/CFT) in the winter. The focus will be on applications in particle theory including $N=4$ SYM, the viscosity/entropy bound, and ...
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Mathematics of AdS/CFT

To date, what is the most mathematically precise formulation of the AdS/CFT correspondence, and what are the most robust tests of the conjecture?