Laurent S. has kindly brought my attention (through Facebook!) to a Leiden University press release and related news in the media:
The main hero of this story is Jan Zaanen, a relatively senior Dutch condensed matter physicist whom we know from String Theory: a Middle Way. Co-authors are Mihailo Čubrović and Koenraad Schalm who has also co-authored other papers with people like Brian Greene, Gary Shiu, or Jan de Boer.
So if you want to divide the physicists into two simple groups, namely the serious ones and the media-driven freeloaders, they're unquestionably in the group of serious physicists! ;-)
Still, the press release is manifestly affected by some journalistic considerations. What do I mean? Well, first of all, it is not true that the papers described in press releases are necessarily the most important papers in the world - and you shouldn't allow other people's self-promotion or biased journalists to think otherwise. Second of all, their work is placed into the context of "string wars". It was a social phenomenon in which the media have blown up the importance of two narrow-minded haters of theoretical physics (and their asslickers) out of any reasonable proportion.
No real physicist has ever been influenced by the tirades written by these two Gentlemen. Everyone in the field knows that their writing has nothing to do with the actual scientific questions and arguments that are being evaluated and improved by the scientific community or the actual changes in the degree of their optimism or pessimism. Nevertheless, the public is gullible enough and many ordinary people still believe that the "string wars" were a phenomenon affecting real science - rather than what they really were, namely a nonsensical media-created bubble building on two pseudointellectual kibitzers.
If you don't know, string theory has won the string wars and the two haters of theoretical physics have largely become invisible after a year of a mad hysteria that has become uninteresting for the readers because they're still much more sensible than what many dumb journalists seem to believe. Nevertheless, theoretical physics has been hurt in the eyes of the most gullible members of the broader public, much like the World Trade Center was hurt by the Muslims back in 2001, despite the bold proclamations that they have actually strengthened the U.S. ;-)
So the enemies of physics have won, too. Much like the hijackers above Manhattan who didn't believe that they would survive and become the real winners in this world, the enemies of physics never intended to do anything more than to hurt someone else, either. And they have done so.
More generally, the episode has shown that it is likely that the media are able and willing to distort the very essence of reality in their goal to create (fake) stories and they do influence the broader society. Such things will probably occur with an increasing frequency and they will be increasingly hurting our civilization.
Condensed matter physicists are a respected subgroup of physicists. Their culture and values differ from those of high-energy theoretical physicists but there are many aspects in which the two groups overlap. The Renormalization Group - the idea to organize phenomena according go the length scale or time scale - was the first deep insight that has really brought the two groups on the same frequency.
The AdS/CFT correspondence is becoming another "shared honey". I have discussed closely related questions in
Now, there's a lot of confusion among the laymen about the question whether the AdS/CFT correspondence is exact and/or proven. First of all, these two adjectives are different: many people don't realize even this fact.
In the case of rather well-defined backgrounds, especially one involving the N=4 gauge theory in d=4 or the AdS5 x S5 background of type IIB string theory, the AdS/CFT correspondence could actually be proven mathematically: see e.g. the approach by Berkovits, Vafa, and others.
But truth to be said, the community is not thrilled by these attempts (even though, it may be said that I am!) because pretty much everyone considers the validity of AdS/CFT obviously true, given the overwhelming amount of partial evidence that is distributed over 5,000 papers or so. In the most popular case, one side - the N=4 gauge theory - can arguably be defined rigorously.
The other side can be fully defined at least perturbatively (and we probably know about most of the nonperturbative phenomena, too, at least qualitatively). The statement that the duality holds is already extremely nontrivial even if we only knew the perturbative part of the type IIB stringy (and gravitational) description. And all the tests suggest that this duality holds and it holds exactly. Because of this reason, we may define type IIB string theory on this background using the gauge theory. This definition is full and nonperturbative.
The less supersymmetry we have, the harder it is to define both sides and to calculate some physical quantities exactly. But a lot of evidence exists for many other backgrounds, too. In fact, many people believe that every field theory has an AdS-like dual, every AdS-like background has a non-gravitational dual, and so on. I am actually uncertain about some of these statements but let me assure you that I am no extreme person concerning my degree of "belief" in the robustness of various hypotheses that have been "largely proven".
The importance of AdS/CMT
The AdS/CFT duality may be applied to non-gravitational theories resembling theories studied by the condensed matter theorists (CMT) and sometimes even the condensed matter experimenters. In this setup, the duality manifestly becomes a new powerful tool to systematically calculate (using new kinds of expansions etc.) the results of complex situations with many particles in strongly coupled condensed matter systems.
Much like in the case of heavy ion physics, this string-inspired method is more accurate, more doable, and more insightful than other known methods, at least for certain classes of questions.
At the same moment, the holographic duality also tells us something about quantum gravity: its elementary degrees of freedom may look like the ordinary degrees of freedom in quantum condensed matter systems as long as you deal with the additional dimensions etc. in the way that the stringy holography dictates.
The new Leiden paper
I won't pretend that I am a world's leading expert in AdS/CMT. There are roughly 50 people in the world who can evaluate new papers about AdS/CFT papers applied to superconductivity "approximately as well as" the authors of the new paper, and I could be roughly 250th in the world which would not be a terribly good ranking because a real expertise in this discipline also requires a more detailed knowledge of condensed matter physics than I can offer. ;-)
Still, at least, you can get a rather fair interpretation what's going on from me.
Superconductors allow the electrons to move without any resistance. We have phenomenological theories (e.g. the Landau-Ginzburg theory) how superconductors behave and we have some microscopic explanations why they work (especially the BCS theory). These microscopic explanations tend to work for ordinary, low-temperature superconductors only.
There also exist superconductors with unexpectedly high critical temperature - and people also want to further increase the highest temperatures where superconductivity is possible at least to room temperatures which would be useful in so many applications. At any rate, even with the "moderate" high-temperature superconductors, there has been no good microscopic explanation why they actually work. You should understand that for condensed matter physicists, such questions are as close to the "holy grail" of their field as many well-known questions in particle physics are the "holy grail" for particle physicists.
(No one has criticized the condensed matter physicists for a "slow progress" of developing and describing the high-temperature superconductors even though it's been slower than anything in string theory. I don't suggest that you start to criticize condensed-matter physicists: the progress is what it can be given the objective state of science and the society. There is no objective "benchmark" setting the right absolute speed in science; only the falsification of ideas and the relative progress in two directions can matter. Instead, I want to make it even more clear than ever before that the critics of string theory have been dishonest imbeciles.)
The Leiden group has used the AdS/CFT methods to study the "critical state of matter" that makes high-temperature superconductivity possible. They start with a Lorentz-invariant, relativistic vacuum; add a high density of fermions to deviate away from the relativistic state; solve the dual Dirac equation in the background of an AdS charged black hole; and find a phase transition between the critical state and a Fermi liquid where a quasiparticle disappears, without changing the symmetry patterns of their theory in any way.
You will have to read the paper to learn more technical details. Some time will be needed to see whether the AdS/CMT experts feel genuinely enriched.
Known and unknown shores of the ocean of ignorance
But I still want to add a few more general words. In physics, we have always thought of "freely propagating" elementary particles to be the fundamental building blocks. And we have always thought that whenever we make the number of particles large or make them strongly interacting, the problem may become extremely messy, obscure, non-fundamental, uninteresting, and uncalculable.
During the duality revolution started in the mid 1990s, this expectation has been significantly transformed. In fact, these days, we think that it is at least morally wrong. Almost whenever you make the number of particles or the number of colors or the coupling constant or any similar parameter very large, you end up with a physical system that looks familiar - like one of those solvable systems you have known for some time. Or a new one which you should have known but you were forced to add it today, learning that it is as natural and consistent as the old ones and it shouldn't have been missing in your classification.
In other words, quantum theories tend to have various classical limits whose "good degrees of freedom" and "basic processes" are rather transparent. These well-defined states of matter can be interpolated by a full theory with an "intermediate coupling" which are really difficult. But their complexity is still "bounded" as the complexity of any system that can be continuously deformed to a very familiar configuration of matter with well-understood laws of physics.
In particular, superconductivity is a pretty robust, general, and clean state of matter. The microscopic details of different superconductors differ but they clearly share "something" and this "something" turns out to admit a good universal description. An effective long-distance field theory was thought to be the only answer.
But the stringy holography allows you do go beyond this point. It makes the separation of physical phenomena to different scales "geometric" (the scale is reinterpreted as the radial coordinate of an AdS-like space) and pretty much transforms the flows from one theory to another theory to a problem that is calculable by Einstein's equations from general relativity and its generalizations. The resulting "bulk" picture contains familiar objects such as black holes and branes. Their possible behavior is known from quantum gravitational physics and allows you to make a lot of conclusions that would be very hard without this bulk description.
All these things are neat and important. They show that seemingly non-gravitational systems are equivalent to string theory in various highly curved backgrounds and the classification of critical states of matter is de facto equivalent to the classification of various special "loci" in the stringy landscape.
Nevertheless, we live in a nearly flat world which is different from the highly curved AdS-like backgrounds that are directly relevant for superconductors and similar physical systems. However, this fact doesn't mean that the real world is based on a "different theory". It is actually the same theory: just the background or, if you wish, the "initial conditions" are different. In fact, they don't have to be quite different. The knowledge about the superconductors and/or high-energy accelerator physics just constrains different parts of the underlying geometry - e.g. the AdS space at different levels of depth.
All these things are still connected either by direct geometry or by various increasingly well-understood phase transitions or at least by the same equations (or the same consistency criteria) they have to obey. Such a network of geometric and mathematical links between previously unrelated phenomena are another general manifestation of unification in physics, too.
And that's the memo.