Since the discovery of the AdS/CFT correspondence in 1997, some physicists (including me) tried to prove it. I am talking about the most famous case with the \(AdS_5\times S^5\) background of type IIB string theory that is described by the boundary CFT in \(d=4\) with the \(\NNN=4\) supersymmetry. And I am talking about some sort of a "direct proof", at least in some regime – there is a lot of circumstantial evidence that Maldacena's duality is correct, of course.Freedom of expression increasingly under attack: the Czech Wikipedia, along with the German, Danish, Slovak ones, and others, is darkened today to protest the March 26th EU-wide vote about copyright laws that would make it mandatory to preemptively search for potential copyright violations in excerpts from news. With worries like that, most sources – except for some monopolies with big legal teams – could indeed be silenced. Freedom to talk about the news is far more important than anyone's copyrights related to news.

*If you "thicken" propagators in a gauge theory Feynman diagram, it starts to look like a piece of a plane – which may be considered a world sheet – cut to pieces. Many things may be done with this 't Hooft picture which was the precursor of holography in the mid 1970s. Well, maybe Nathan wants to add at least one reference to a paper by 't Hooft LOL but I understand what's behind such omissions.*

That duality is usually studied for a large gauge theory 't Hooft coupling where the radius of the AdS space and the five-sphere (the radii are equal) is much larger than the 10D Planck scale in the bulk quantum gravitational theory (type IIB string theory). But at some level, the correspondence should be true for a small radius as well, i.e. for the highly curved AdS space that cannot be easily described by a low-energy "classical" gravitational action.

You may Google search my blog for a proof of AdS/CFT – this topic is very old. Also because I am being acknowledged (thanks, Nathan) although I didn't give him any useful input recently, I sort of have to write about (my once co-author's and brilliant physicist's) Nathan Berkovits' new iteration of the proof:

Sketching a Proof of the Maldacena Conjecture at Small RadiusIt's still a "sketch" so we don't know whether it will be treated as the "final word" on these proofs sometime in the future.