In recent years much of the attention of string theorists has turned to applications of string theory (via AdS/CFT) to heavy-ion physics and condensed matter physics. Since I’m no expert on either topic, I’ve been curious to hear what experts think about this. In the case of heavy-ion physics, as far as I can tell, this doesn’t seem to have worked out very well, with string theory not of much use to say anything about heavy-ion physics at the LHC (although I’d be interested to hear from those more knowledgeable about this). There does still seem to be some promotional activity in this area, with Joe Polchinski last month giving a popular talk in which he claimed that
The quark-gluon liquid, produced at the RHIC accelerator in NY and by the LHC, is best modeled as a black hole, by applying AdS/CFT duality.
On the AdS/CMT front, one expert is now being heard from. In the latest Physics Today, Philip Anderson has a piece called Strange connections to strange metals, in which he responds to an earlier Physics Today article by Hong Liu, From black holes to strange metals, which claimed:
String theory relates gravity to the physics of a novel phase of matter observed above the superconducting transition temperature.
Anderson writes:
It [the earlier Physics Today article] is one of many quasi-journalistic discussions I have seen of results using the AdS/CFT (anti–de Sitter/conformal field theory) correspondence from quantum gravitation theory ostensibly to solve condensed-matter physics problems such as the “strange metal” in the cuprate (high Tc) superconducting metals. As the probable source of the buzzword phrase “strange metal” to describe the phenomena observed in the cuprates and of a theory that bids well to explain those phenomena in detail, I think I have a reasonable motivation to object to the publication of those claims, even though advanced tentatively, when so much is known about this particular phase.
He ends with a summary of what he sees as the problem with the whole AdS/CMT idea:
As a very general problem with the AdS/CFT approach in condensed-matter theory, we can point to those telltale initials “CFT”—conformal field theory. Condensed-matter problems are, in general, neither relativistic nor conformal. Near a quantum critical point, both time and space may be scaling, but even there we still have a preferred coordinate system and, usually, a lattice. There is some evidence of other linear-T phases to the left of the strange metal about which they are welcome to speculate, but again in this case the condensed-matter problem is overdetermined by experimental facts.
Hong Liu responds here.
Anderson will be here at Columbia to give a colloquium April 15 on The Discovery of the Anderson-Higgs Mechanism. I’ve written something about this history here, look forward to hearing about it from Anderson himself. There’s much speculation about a possible Nobel for the Anderson-Higgs mechanism this year, one wonders if the Nobel committtee has any AdS/CMT proponents…
Update: An additional comment about this just occurred to me: the criticism of Anderson’s work on the Anderson-Higgs mechanism has always been that he didn’t appreciate how different relativistic systems. Now he’s claiming the AdS/CMT proponents don’t appreciate how different non-relativistic systems are.
Hi Peter,
Sachdev has written about this connection. He has some articles on his website: http://sachdev.physics.harvard.edu/
I think the key point here is explained in the last paragraph of Liu’s response:
“Whether or not one finds a ‘conventional’ explanation for strange metals, connections between the physics of strange metals and black holes are worth exploring. They hint at a new paradigm for thinking about strongly correlated quantum soups. As an added bonus, we may also obtain new insights into quantum gravity from advances in condensed-matter physics.”
Research into the AdS/CFT correspondence is important not only because of its potential applications in condensed matter physics. It’s also a very important general idea in quantum field theory, and it has led to important insights into the holographic nature of quantum gravity.
I believe the key test in science is falsifiability:
Is there an experimental outcome (realizeable or Gedanken) that would mean that “strange metals cannot be described by a theory with a classical gravity dual”?
If not, then AdS/CMT is essentially a very fancy way of parametrizing data, rather than a physical theory.
The fact that most such work is based on “bottom-up” potentials chosen by hand makes it likely this is indeed the case, but the jury is still out.
Replying to lun’s comment, it is an interesting thought exercise to replace “theory with a classical gravity dual” with “effective field theory”. Like any particular effective field theory, any given theory with a classical gravity dual of course produces falsifiable predictions. It is a rather formidable enterprise to falsify the framework of effective field theory. (Perhaps we should try.) Nevertheless, I think there is general consensus that effective field theory is a very useful framework for describing the world we live in. Gauge/gravity duality promises to become (or perhaps already is) a somewhat less general although nevertheless very interesting framework in which to write down specific physical models.
The EFT analogy is indeed often used, but I think it is flawed.
The applicability of any generic EFT has a stringent well-defined
set of requirements:
A hyerarchy of scales (the “typical scale”<<"the fundamental scale"), and
a stable vacuum.
It is usually very easy to see whether a system fails at these characteristics,
and there are plenty of systems where applying any EFT, intended in the conventional way, is plainly foolish (turbulence, glasses, phase boundaries with EFT of
one phase. Of course sometimes people try to apply EFT to domains where it clearly fails, but this is a problem of EFT practitioners, not EFT itself).
From what I can see very little effort is being made to define
a similar domain of validity for AdS/CMT.
Note I am not saying it is impossible to do, simply it is not considered
an important problem, and is generally disregarded: For instance, one
obvious criterion for the validity of the classical gravity description is that
N, the number of YM colors, is large. Yet there are well-cited papers by
famous people who attempt to model 1/N effects by classical gravity
descriptions. There is a fundamental issue there, 1/N corresponds to
deviations from classical gravity, but this is usually not even mentioned
in the paper.
Part of the reason is objective difficulty: For almost all systems
where Gauge/gravity is used, we do not know the the Gauge theory.
For bottom-up systems, which seem to form the basis of AdS/CMT models,
we dont know either the Gauge or the Gravity description.
But it is still bothersome that some people who do this essentially use
some complicated AdS concoction to draw a line through a bunch of data,
and then say "this system can be described by string theory".
lun,
I think Anderson is wisely not getting into very general arguments about falsifiability, but addressing the question of whether, in this particular case, AdS/CMT methods give a better or worse model for the system in question. It seems to me that his claim is that he and others have models that explain much more about these systems than the AdS/CMT-based models. If so, publication of articles aimed at non-experts claiming that the way to understand this physics is via strings, quantum gravity or black holes (even in the case of Polchinski and heavy ions, that the system is “best modeled” this way) is quite misleading.
The hype level in the past associated with AdS/CFT methods has been very high (these supposedly provide the “harmonic oscillator” of the 21st century…). No one would object to people pursuing ideas about use of such methods in condensed matter theory (“falsifiable” at this stage or not), as long as they’re not misleading people about how well their methods work compared to others.