# Introduction to AdS/CFT

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AdS/CFT seems like a really hot topic and I'd like to start reading about. I am looking for the best introduction at my level, i.e. I have a background in QFT, CFT and general relativity at the level of a master student in theoretical physics. What would you recommend me to start tackling the subject? I have been looking for resources and so far I have noticed:

-this synthetic introductory lectures by Horatiu Nastase: http://arxiv.org/abs/0712.0689

-the videos of lectures done by P. Vieira at Perimeter for Perimeter Scholar International students: http://www.perimeterscholars.org/341.html

-the subject starts entering the most recent textbooks on string theory. We have the Schwartz and Becker ( http://goo.gl/jh45U ) and also the Kiritsis ( http://goo.gl/ulEVw )

I probably missed a lot of resources, as the literature on the subject is already quite huge. I would really appreciate some advice on that, as I already had the frustration of losing my time on not-so-good books when started to learn something new, so if I could (to the best) avoid that this time...

This post imported from StackExchange Physics at 2014-03-24 05:04 (UCT), posted by SE-user Just_a_wannabe

asked Sep 13, 2012
recategorized Apr 24, 2014
I would also like to add: String Theory Demystified by David McMahon, Chapter 15 link. I liked it as a good starting point to get a good overview without loosing to much time.

This post imported from StackExchange Physics at 2014-03-24 05:04 (UCT), posted by SE-user ungerade

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You may find a list of reviews under the item Anti-DeSitter Space in the nice website "The Net Advance of Physics"

There is a nice review of the applications of gauge/gravity duality to the heavy ion collisions Gauge/String Duality, Hot QCD and Heavy Ion Collisions

This post imported from StackExchange Physics at 2014-03-24 05:04 (UCT), posted by SE-user unstable
answered Sep 13, 2012 by (0 points)
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There is also this set of lecture notes from Raman Sundrum: 'Fixed Points to the Fifth Dimension':

http://arxiv.org/abs/1106.4501

This post imported from StackExchange Physics at 2014-03-24 05:04 (UCT), posted by SE-user DJBunk
answered Sep 13, 2012 by (80 points)
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Thanks for the links above. After pursuing my research I found this quite exhaustive bibliography linking to online resources:

I hope it won't be useful only to me ;)

This post imported from StackExchange Physics at 2014-03-24 05:04 (UCT), posted by SE-user Just_a_wannabe
answered Sep 15, 2012 by (30 points)
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I had to give a talk on AdS/CFT without knowing anything about it beforehand, and I found this set of lectures by Johanna Erdmenger extremely accessible: http://wwwth.mpp.mpg.de/members/olivers/AdSCFT-2010-01-22.pdf

It's also now part of a nice book of lectures string theory edited by Michael Haacke, Ilka Brunner

This post imported from StackExchange Physics at 2014-03-24 05:04 (UCT), posted by SE-user Judy Kupferman
answered Sep 19, 2012 by (0 points)
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The point of view of algebraic quantum field theory is given by K.-H. Rehren, hep-th/0411086. His paper defines the correspondence fully within QFT, without the need of any background knowledge of string theory. (The applications to QCD don't make use of the connection to string theory either.)

answered Aug 26, 2014 by (15,488 points)

Huh, then how is the AdS side where one has quantum gravitiy discribed by this approach? In this answer, Lumo explained that QFT approximations, such as SUGRA are only valide for large t'Hooft coupling $\lambda\equiv g_{\rm YM}^2 N$ and small curvature of (the backround) spacetime. Does this algebraic QFT aproach work for all values of the t'Hooft coupling?

Intrinsically, AdS/CFT has nothing to do with gravity or supersymmetry, although it was found in this context. It is simply a way to get a 1+3D conformal field theory from the boundary of an AdS field theory. The article by Rehren makes this clear. For applications to QCD  this is enough. Since (currently only) this is the contact of AdS/CFT to experiment, I (currently only) investigated this application.

I don't know enough about quantum gravity ans string theory to say something meaningful there. Thus I cannot answer your question about gravity and strings alluded to in the answer by Lubos Motl. Can't you ask him there?

Hm, I am not sure if saying the QCD application of AdS/CFT is the only contact to experiment is a bit too pessimistic ... I will ping Lumo below my P.SE question about the issue to try to bring him back here ...

I added the qualifying word ''currently''. This may change in the future, e.g., if supersymmetry is experimentally detected. (But I am happy enough if I understand the standard model, and have no ambitions beyond that.)

It is a non-sense to say that AdS/CFT has nothing to do with gravity. Another name, a bit more general, of AdS/CFT is gauge/gravity correspondence, with a gauge theory on the boundary and a gravity theory in the bulk. As correctly recalled by Dilaton, for large t'Hooft coupling, the true quantum gravity (i.e. a string theory) reduces to its low energy effective limit, i.e. a supergravity theory. Even in this limit, the theory living on AdS is a gravity theory, it is even in first approximation classical gravity theory. This is absolutely necessary for the duality to work: the dual of the stress-tensor operator of the gauge theory on the boundary is the metric in the bulk, i.e. to compute correlation functions of the stress-tensor in the gauge theory, one has to solve supergravity equations with appropriate boundary conditions. In the "applications" to the quark-gluon plasma, applying the above procedure shows that the dual of a plasma is a black hole in AdS and the results experimentally testable on quark-gluon plasma come from our knowledge of black holes. It is difficult to find something more gravitational...

As you say, gauge/gravity correspondence is something more general than AdS/CFT: The latter is a more special situation independent of gravity - the AdS metric is completely fixed and not dynamical.

The paper by Erlich http://link.springer.com/article/10.1007/s00601-011-0292-z discusses both the gravity-induced top-down approach and the gravity-free bottom-up approach. It is the latter that is computationally useful and gives formulas with a testable content. The action (2) used contains no gravitational field, only the fixed AdS metric that comes from the group.

Erlich's more recent arXiv paper http://arxiv.org/pdf/1407.5002.pdf pays more lipservice to gravity, but nevertheless the Lagrangian (4.16) that is responsible for the QCD physics (''bottom-up holographic QCD'') again simply works with the fixed and classical AdS metric. Only the more speculative top-down Section V has a gravity-related duality but its connection to experiment is not established.

There is nothing in principle "untestable" about the more wide spread notion of AdS/CFT either...

In principle, you are right. But Erlich writes in the introduction to the first cited paper: ''The benefit of bottom–up models is that there is more freedom to build in properties of QCD.'' - One apparently needs this freedom to get properties close to the real world. Essentially, rather than restricting a string theory or supergravity theory, one creates an action in AdS space that has just the observed structural content and parameters that can be fitted to the observed hadron spectrum, say. Without this fitting freedom, the fit would apparently be poor.

Thus the AdS action is just treated as an effective action. A string or supergravity theory would have to produce this effective action, but at present, this seems to be out of reach.

Nah, I would say out of reach is a bit a strongly negative term, I would rather say it is in principle doabel, but very difficult. Probably similarly as to the problem of extracting the standard model, the space of solutions to ST have to be better understood first. I personally like explanations from first principles better than just fitting parameters to data.

Physicists try to do both, of course - trying derivations from first principles and trying to match the data with effective theories. The former is over my head. For the latter, the AdS/QCD version in http://arxiv.org/abs/hep-ph/0602229 (which includes a scalar dilaton field but still no dynamical gravity) seems currently quite reasonable. Perhaps both approaches meet one day.

@  Arnold Neumaier: you write "as you say, gauge/gravity correspondence is something more general than AdS/CFT: The latter is a more special situation independent of gravity - the AdS metric is completely fixed and not dynamical." What is usually called AdS/CFT is a gauge/gravity correspondence with a full gravity theory on AdS. If someone wants to consider something else then it is better to find a different name.

It is true that some calculations, as the one in the paper you cite, can be done with a fixed metric  on AdS but these are only approximations. Of course, it is perfectly fine to do such computations which reduce to usual QFT on a fixed curved spacetime but it is necessary to remind that these are approximations. In the second paper of Elrich, he writes correctly (at the end of page 6) "In known holographic dualities, the higher-dimensional version of the theory always contains gravity, and the failure of the intuition that fewer dimensions implies fewer degrees of freedom is related to some unusual properties of black holes in general relativity".

It is a general consequence of the holographic principle that the dual of the stress-tensor operator of the gauge theory on the boundary is the metric in the bulk. So if there is any non-trivial excitation in the gauge theory, there will be some non-trivial excitations of the fields on AdS which will in particular modify the metric. For some questions, it is possible to neglect this backreaction of the metric, what is done in the papers you cite. For some others, it is not possible. For example, the dual of a thermal plasma is a black hole.

''If someone wants to consider something else then it is better to find a different name.'' It is not me who chose the terminology. In all papers I saw comparisons with to actual data, it was always called AdS/CFT (occasionally in addition AdS/QCD) and it was always computed in a fixed metric. No use was made of gravity, and the basic principle can be understood without it. In the sense of duality as two essentially different descriptions of the same theory, these are already dualities.

''it is necessary to remind that these are approximations'' - to the bigger theory, of course. But who knows if the bigger theory is exact - all of physics is approximation, unless you just study a particular theory and take it to be exact.

@40227 thanks a lot for these nice explanations!

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