What are the achievements of AdS/CMT ?

It seems too early to say.

Subir Sachdev wrote a review, and gave his opinion in a recent talk at the Perimeter.

My own favourite direction is Swingle's conjecture about MERA and AdS/CFT.

 

There're lots of work trying to calculate the properties of condensed matter using an asymtotically AdS black hole. However, I think all these attempts lack a proof, and what they actually do is just pick a small part off the whole curve and claim this part gives the correct result.

 

In my opinion, honestly, not much so far. Certainly in the context of solid state physics there hasn't been much impact.

On the other hand, we're still getting our feet wet, and furthermore, some nominal string theorists have made meaningful contributions to condensed matter physics. Certainly holographic duality informs their perspective, although I can't say that the work is ultimately very holographic.

Part of the problem, in my opinion, is the differing goals of stringy people and cond mat people. For example, cond mat people tend to care a lot about UV completions and actually identifying a plausible material or model which displays the phenomena of interest. On the other hand, sometimes I think string theorists are allergic to "non-universal physics". To take a particular case of recent interest, the low energy physics of a topological insulator has been known, as a field theory, for a long time. The idea of robust boundary states has also been known for a long time e.g. in lattice gauge theory as a way to get chiral fermions. And frankly, as a field theory the whole thing is rather trivial. As far as I can tell, the excitement in cond mat only really appeared when these things were proposed to be realized in concrete models and then seen experimentally. And I don't want to say that cond mat people have it all right, since in my opinion, as in this case, they often get excited about fairly trivial things. Trivial is here used in its technical sense meaning "not very interesting from the perspective of the deep principles of physics" :)

But one thing holographic duality has had a big impact on, at least for me personally, is entanglement. Also, holography has been relatively successful as an idea generation machine i.e. suggesting new phases, dynamical phenomena, points of view, etc., ideas that are slowly beginning to get a foothold in cond mat.

This is all to say that the relationship is complex but interesting. I think its a great thing to dabble in, at the least, and the main thing I would suggest is to find some real cond mat people and listen to them a little bit (and make them listen to you!).

 

It has a bright future I hope. :)

 

Brian, do you have any comments about the new paper by Nozaki, Ryu and Takayanagi (arXiv:1208.3469)? The whole idea is extremely interesting.

 

Yes, it is a nice attempt to formalize the ideas of my original paper in the continuous setting. I'm writing a new paper on the subject, and their definition gave me an idea for a slightly refined statement. So it has already influenced my thinking.

I also like their attempt towards dynamic phenomena e.g. quantum quenches and the attempt to partially understand diffeomorphisms from the RG perspective. Such a relation has always been expected, but it is particularly unclear what's going on in the context of different time slicings of the putative bulk. So any insights are welcome.

 

Are you B. Swingle?

 

Yes.

 

Yes. The earliest papers considering different kinds of scaling symmetries in holography were http://arxiv.org/abs/0804.4053 and http://arxiv.org/abs/0804.3972. One can also break conformal invariance by adding a chemical potential. There have been many subsequent developments.

 

People think so, but to actually proof that this is possible needs an explicit embedding into string theory. This has only been proven for a few relativistic cases.

To see the subtleties for non-relativistic holography, check the notes of Hartnoll. A difference is that you need codimension two instead of one, which can be traced back to the non-rel. algebra as Hartnoll explains.

What people usually do is to consider solutions of the relativistic field equations with non-rel. isometries. Very few people have considered taking actually non-rel. gravitational theories. These can be written in general-covariant form known as Newton-Cartan theory. The EOM can be derived from a Hilbert-like action (which of course is crucial for holography!), but for this you need to introduce an extra dimension (related to the fact that the D-dim. Galilei algebra can be embedded in the D+1-dim. Poincare algebra) and perform a so-called "Bargmann-lift". This also explains the extra codimension you need on the gravitational side from another point of view. One problem is that these Newton-Cartan formulations only have naked singularities as solutions instead of black holes. To read further, see e.g. http://arxiv.org/abs/0810.0227.

 

I have to slightly disagree. I don't see any reason why string theory should be considered the ultimate arbiter of correctness especially since we don't even know what it is.

Also, a lot of interesting non-relativistic or condensed matter physics can be obtained via relevant deformations of a CFT. One simply has to perturb it via a chemical potential or magnetic field, etc. Certainly we know many string theory versions of this story.

 

Two papers today, by Janiszewski and Karch, on Horava duals for a broad class of nonrelativistic QFTs, and how to embed them in string theory.

 

Well, in the original proof of the duality between N=4 SYM and type IIB String Theory one crucial ingredient is e.g. D-branes. In the duality you need ingredients of string theory as we know understand them, so I don't get your argument that "we don't know what it actually is". That's true, but to write down an explicit mapping we need to show the relation between objects in one theory and the other.

Could you give some explicit examples and references?