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After almost 20 years of AdS-CFT, what have we learned?

In QFT we can’t generally do strong coupling regimes, however AdsCFT has helped obtain results that would be impossible with QFT alone in this regime.

AdSCFT gives insight into connection between information and area laws. Can we export ideas from here to other areas?

Is it assuming SUSY which so far we have not observed in LHC experiments?

It allows us to connect the structure of entanglement in a conformal field theory to geometry and structure in the bulk. This may help in formulating the emergence of space-time.

A problem is that AdS-CFT is most robust for non-physical theories. Its application to more realistic theories appears much more speculative. Can something similar to ads CFT apply to realistic theories?

Suggestion that degrees in the surface are important for describing the bulk eg. connection between entanglement area laws and area laws in the boundary (e.g. black hole entropy).

Almost 20 years have passed since Juan Maldacena enunciated what is known today as the AdS/CFT correspondence.  This correspondence has not yet been proved but there is an immense amount of theory that suggests that this correspondence is valid.

One of the main teachings of such a correspondence is that it somehow saves the fate of string theory as a physical theory, rather than a mathematical theory. The reason for this is that the correspondence offers a path for string theory to be tested experimentally, since there are experimental predictions that are testable in the CFT side. However one can argue that the correspondence itself is not of much use when describing the universe since the observable universe appears to be dS instead of AdS. Apart from this, there are several other teachings from this correspondence. A very important one is the fact that space-time is not fundamental, but it can be an emergent thing.  Furthermore the AdS/CFT correspondence seems to be just a very interesting realization of a more general and underlying holographic principle. Finally, the correspondence has proven itself to be a very useful tool in several fields of physics. It can be understand as 'change of basis' in which certain problems can be addressed in a much simpler way. An example of this is offered by the strongly correlated systems which find a natural explanation in terms of a corresponding holographic dual.

The main results are a better understanding of what the fundamental degrees of freedom could be in a theory of quantum gravity. This understanding moves beyond local quantum field theory. Several critical points that were raised included (a) our universe is nearer to dS than AdS, (b) an important problem of quantum gravity is to understand the structure of space and time and for that one should know more about bulk reconstruction, that seems to be a key difficulty in AdS/CFT (c) some fundamental issues cannot be resolved for instance the problem or nature of time in circumstances where one does not have a boundary.

It was pointed out that AdS/CFT is more about learning new patterns, which teach us much more about the nature of quantum field theories. The question was raised of what constitutes as ‘fact’ in AdS/CFT.

QG in AdS needs string on world sheet. If u take Ads-CFT as the definition of QG, AdS-CFT is an argument that string theory is a good candidate for QG.

It also can used to tell something about QG in flat space (working with AdS with large radius).

AdS-CFT gives a physical interpretation for confinement-deconfinement. It complements the study of gauge theories.

Applications of AdS-CFT: heavy ion collision. Condensed matter. QCD calculations. Understanding strongly coupled QFT.

Use of toy models

Not typically realizable

Turbulence on the gravity side?

Mistake to think that there’s only one quantum gravity
How to interpret symmetries / what they mean can be very different

What about quark/gluon plasma?  Status

Inspiration to people in field…

How do we get beyond the conjecture stage?  Matching observables on each side is fruitful

Are the most interesting theories the ones that violate the conditions

AdS/CFT makes holography feel much more real. It gives us reason to believe that the holographic principle is a true principle of nature. However, it is only a very specific case. We think holography should be applicable in much more general cases. For example, the CFT side of AdS/CFT is very unrealistic, and the conformal symmetry must be relaxed for most practical, real-life applications. Another very important thing that we have gained from AdS/CFT is the interaction between different fields of physics. Without AdS/CFT, string theorists and condensed matter theorists, for example, would not have interacted as much as they do now.

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