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I will begin my research on AdS/CMT, however I find AdS/CMT is only a phenomelogical method, so I want to know can AdS/CMT give some results the condensed matter physicists can not give, or even predict some unseen exotic matter states?

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do you mean to say "ads/cft"? –  user346 Feb 26 '11 at 15:00
also if your question is "are there condensed matter applications of ads/cft", I believe a similar question has been asked before so this might be a duplicate. –  user346 Feb 26 '11 at 15:16
Near Deepak, no, lijun writes CMT so he or she means CMT, not CFT. It's Condensed Matter Theory. ;-) –  Luboš Motl Feb 26 '11 at 16:56
Yes, Condensed Matter Theory is an entirely separate priesthood :) –  Gordon Feb 26 '11 at 19:11

2 Answers 2

I'm not an expert on CMT applications of AdS/CFT aka gauge/string duality so you might get a better answer from such an expert. The idea of applying this formalism to condensed matter systems is quite recent and most of the work has been done in the last 1 1/2 years. So far I don't think there are any spectacularly new results of the type you are asking about, but I think many people hope there will be eventually. Certainly this is a new technique for studying strongly coupled condensed matter systems so in principle it may allow you to understand things that other techniques do not and perhaps even predict some exotic state of matter. Presumably one of the reasons you are starting research in this area is to answer such questions. Perhaps you will report back and answer your own question in a few years.

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I've worked some on AdS/CMT so I can discuss a bit some of my motivation.

As Jeff points out, we have now a fundamentally new technique to studying strongly coupled systems, so it makes sense to use it to attack any problem under the sun that needs new tools. At our current level of understanding, as you point out, the best we can hope for is constructing phenomenological models for interesting physical phenomena. Part of the price to pay for holography is that the usual description (say in terms of band electrons interacting in a specific way) gets highly scrambled, as it should for a more physical description of strongly coupled systems. But, it is then hard to identify specific models for specific materials, and one has concentrate on qualitative and semi-quantitative physics. I think this is the nature of the beast and currently there is no way around it.

On the other hand, I think that CMT is particularly well-suited for this approach, precisely because the phenomenological models are normally the best you can hope for in such inherently complicated problem. For example, when people work on the Hubbard model it is because it is expected to capture some of the features important in high Tc superconductivity, not because it is in any way related specifically to any real material. I can certainly see AdS/CMT reaching this level of usefulness.

So, along those lines I'd say the best that has come from AdS/CMT so far is a fairly natural description of superconductivity, a large class of quantum phase transitions, and some work on non-Fermi liquids which seems to be related to strange metal phenomenology (e.g all the marginal Fermi surface phenomenology and some indication of the right scaling of transport properties). Probably better results are yet to come, which is why this is a good subject to be working on.

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So what's a good reference for the "natural description of superconductivity" given by AdS/CFT? Hand waving and picture drawing is fine for me, I've just been a bit frustrated in the past by folks working in this field - I mean, yes there are neat results, but to us mere mortal CMT folk, we need mechanisms more than curve fitting, and "high Tc superconductivity occurs because of the mathematics of black holes!" is a nip unsatisfying... –  wsc Feb 27 '11 at 4:20
I don't think there are claims directly related to the cuprates, and issues of mechanisms would be difficult due to language barriers, and the scrambling I mentioned. But, there are more modest claims and lots of details (e.g. in Hartnoll's review "holographic methods for CMT"), which go well beyond curve fitting or hand waving. –  user566 Feb 27 '11 at 4:46
Thanks for all the reply!! –  user2268 Feb 28 '11 at 2:38
Sure. Good luck, should be a fun subject to get into. Looking forward to reading your papers. –  user566 Feb 28 '11 at 2:54

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