# Which AdS/CFT correspondences have been found so far?

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When I read about AdS/CFT correspondence, there always comes the most famous example of conjectured correspondence, which is the one between type IIB string theory (AdS side) and $$\mathcal{N}=4$$ supersymmetric Yang-Mills (CFT). I was wondering, if there were other correspondences that are being conjectured out there, but that maybe do not get so much "mainstream" attention?

As I understand it, the difficulty of finding the correspondences is that often one side can be treated perturbatively, while the other side not. In 2D CFT, I believe there are theories (correct me if I am wrong) that can be solved exactly. Was there any correspondence found there? I also heard about the AdS/CFT being a potential solution to the black hole information paradox. Is something specific conjectured here?

I am looking mostly for a list of the conjectured correspondences, if any, but any detail would be highly appreciated.

Edit: following the comment below stating that there might be several hundreds such conjectures, let me restrict the question to the most notable AdS/CFT conjectures, with foreseeable applications in any field of physics, such as for example black holes, superconductors, condensed matter, phase transitions, etc.

This post imported from StackExchange Physics at 2019-07-25 14:14 (UTC), posted by SE-user Jxx
Probably several hundred such dualities have been conjectured. If you care about work in a particular dimension, you can search for it in arxiv, e.g. "AdS3/CFT2" or "AdS4/CFT3".

This post imported from StackExchange Physics at 2019-07-25 14:14 (UTC), posted by SE-user Mitchell Porter
@MitchellPorter Thanks for your comment! Oh really, that many? Then let me edit my question to make it a little more specific.

This post imported from StackExchange Physics at 2019-07-25 14:14 (UTC), posted by SE-user Jxx
I don't think your question has a definite answer. AdS/CFT is a very, very large area. There are 14680 papers citing Maldacena's original paper as of today. Not only are there tons of conjectured correspondences, but there is a point of view that any quantum gravitational theory in AdS is dual to some CFT on the boundary.

This post imported from StackExchange Physics at 2019-07-25 14:14 (UTC), posted by SE-user Peter Kravchuk
@PeterKravchuk Right, but most of the CFT duals are not known, right? I mean, it seems to me that the systematics of AdS/CFT would be easier to study for theories in lower dimensions with exact known solutions, such as some 2D CFTs for example. Or is the supersymmetry of $\mathcal{N}=4$ making it easier than anything else?

This post imported from StackExchange Physics at 2019-07-25 14:14 (UTC), posted by SE-user Jxx
I'm just saying that to my taste your question is very broad, even after the edit:) I'm no expert, but if you are interested in AdS3/CFT2, try looking for D1/D5 system. In general I think that explicit dualities are always supersymmetric. I am not sure if there are exceptions.

This post imported from StackExchange Physics at 2019-07-25 14:14 (UTC), posted by SE-user Peter Kravchuk

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