[Despite appearances, I did not choose the music in what is to follow. I just put on iTunes set to random, and started typing, reporting on what was playing as I went along. Nevertheless, there were some nice resonances.]
So. I must put the Aspen time on hold for a short while, as I promised to give four lectures in Vancouver starting tomorrow. While I sit here in a lounge in Denver at 8:00am, wondering why I booked a 7:00am flight out of Aspen, and also wondering exactly what is in this muffin that I picked up to have with the (rather good) tea they have here this morning, I thought I’d tell you about a little bit of really nice physics that’s going on in the neighbourhoood of my world. Since I’m too cheap and too disinterested to pay for a connection to the web, this’ll only get uploaded quite a bit later when I get a free hookup. (This is a bit more technical in places than usual. Please don’t give up too easily. Oh, and you might have to read some things I point to from earlier to get everything I’m saying – I’m not one for endless repeating myself I’m afraid.)
You can think of this as another story in the line of development I’ve been pushing (and telling people about here and elsewhere) for many years now. Applications of string theory to a broader range of physics areas than the popular discussions of the topic seem to touch upon. I told you last year about the exciting work going on in understanding properties of new phases of nuclear matter being unlocked at the Brookhaven experiment RHIC (colliding heavy nuclei together to create a sort of hot quark-gluon soup). That work continues. This new work pertains to experiments as well, and this time, these are closer to the human scale bench top experiments we all get misty-eyed over (ok, I do, maybe no-one else). It is super-cute stuff. I should hasten to add that, unlike the RHIC/String work, I have absolutely nothing to do with it so far, and certainly made no remarks (insightful or otherwise) about this sort of detailed connection in the past (not that anyone would remember anyway!).
What is this work? It is the study of cold atoms, in a trap. In particular, trapped Lithium atoms in a background magnetic field, scattering off each other. For an appropriate tuning of the field (manipulating the hyperfine level structure such that the scattering length of the system’s constituents exceeds the system size), the blob of trapped atoms can be put into a very interesting phase which is strongly coupled (yes – despite being thought of as a gas). I recommend the review by Immanuel Bloch, Jean Dalibard, and Wilhelm Zerger (see here). (I randomly found some nice online explanations of some of this area of research at Rice’s Hulet group.) It is very difficult to describe using the traditional methods for such systems, and it’s appropriate to look for new tools.
This might sound familiar to what I told you about before. An experimental system that is inherently strongly coupled, some of whose physics seems to be beyond the ability of traditional methods to describe. Then, it was the quark-gluon plasma, which turned out to be a strongly coupled fluid with rather remarkable properties that are nicely described (at least qualitatively) by various string theory models, using what we call “gauge/gravity duals”. The system gets mapped to a ten dimensional geometry, involving gravity and various fields and objects coming from string theory, that is more easily describable and yet yields just the right sort of four dimensional physics – plasmas with the right sorts of properties to do the job.
As Harrison Ford’s character said in the long forgotten Peter Weir movie, The Mosquito Coast, “It is not magic, it’s thermodynamics”.
Actually, that’s not what I wanted to say, but I wanted so much to use the quote so went off track a bit. I meant to say: It is not magic, it is simply a matter of finding the right variables. The right variables for the physics seem to be in terms of extended objects living in ten dimensions. Physics is largely about pragmatism: If that ten dimensional scenario describes your four dimensional physics and helps you understand your experiments, and there’s no sign of something simpler that’s doing as good a job, what do you care?
So here we are again, but there’s at least one very important difference: The system is not relativistic. This is a highly non-relativistic system. So the usual string theories are not going to work quite the same way. The successful duals of last time were based around the AdS/CFT-like systems (variants thereof, but in that spirit), which are inherently duals of relativistic quantum field theories, appropriate to issues in particle and nuclear physics in collider contexts where there’s a lot of stuff banging together and rushing around at significant fractions of the speed of light. Not so here. Instead we’ve got nice, peaceful cold Lithium atoms puttering around in a blob of gas trapped in a trap in a lab. Very non-relativistic. And, relatively speaking, huge. Several orders of magnitude larger than the “traditional” realms of string theory.
The key trick that a number of workers started doing is trying to engineer some dual geometries by following what went before. For the relativistic cases, the prototype is a four dimensional conformal system. It has a particular algebra of symmetries associated to it which generate the symmetries. The dual system has these symmetries realized simply as properties of the geometry (“isometries” – like the group of rotation symmetries SO(3) are manifest in the roundness of a round two-sphere [tex]S^2[/tex], and isometries of the metric on it.). One way to think of how these systems end up being higher dimensional is that to fully geometrize the symmetries, you need more dimensions. This is, from this perspective, how AdS gets involved in describing systems that are conformal (or, as in the hot quark-gluon-type plasma, can be described as broken from conformal in a particular way).
So the idea of Dam Son (see here), and also Koushik Balasubramanian and John McGreevy (see here), was to do the same thing here. Seek geometries that realise the algebra of symmetries purely geometrically. The non-relativistic conformal symmetries are called Schrodinger algebras by some, and they did indeed find such geometries.
The next step was described by Allan Adams in a beautiful talk at Aspen last week (see above picture of him in action – strongly interacting blob of particles conveniently accompanying him…!). How to make this a string theory that we might have some computational control over? In other words, how do we extend this to a fully ten dimensional theory with a family of fields and other objects propagating in it that we have legitimate reasons to believe we can do reliable computations in? They (Adams, Balasubramanian, and McGreevy, see here) found such a geometry (rather, a family of geometries) after a series of solution-generating techniques I won’t trouble you with. [Update: See also papers by Christopher Herzog, Mukund Rangamani and Simon F. Ross, (here), and by Juan Maldacena, Dario Martelli and Yuji Tachikawa (here).] They started with something familiar (actually, the same black hole-like geometry that describes the finite temperature plasmas of the old story) and turned it into a new family of geometries. In doing so, they could also follow what happened on the other side of the duality to figure out (some of) what the field theory description of the dual theory is – It is something that starts out as the Yang-Mills theory but gets horribly messed around by the solution-generating techniques to become something else that is, finally, non-relativistic and much more like the cold atom system.
Interlude. By happy random iTunes circumstance, we have:
Oh, that’s a good song here. You can make up your own jokes at this point… I can just hear the usual bitter string theory haters singing along to this one:
The world has gone mad today,
and good’s bad today,
and black’s white today,
and day’s night today…
Back to the story.
So you get to ask at this point about the atoms. Where the Dickens are they in all this? At least with the quark-gluon system you could point to the stuff in the lab and the stuff on the string theorists’ pages and see something similar on both sides – non-Abelian Yang-Mills theory. So that there are places where these two very different systems might capture similar physics could be imagined, with a bit of squinting. There’s nothing of the sort going on here, so what’s to say this is not just manifestly a red herring?
Well, I should stop you there. For a start, it’s probably lulling people into a very false sense of security to think that having Yang-Mills somewhere on both sides of the story in the nuclear system was really an unambiguous clue to the story. I could unpack this further, but suffice it to say two things for now: (1) QCD, the theory of the nuclear interactions, is *not* supersymmetric Yang Mills with adjoint flavours. Something about some of the gross physics of the system really did not care much about such details though. (The details do matter for lots of questions – that’s what lots of us continue to work on – but it is a really nice turn out that for some of the key general features, they did not as much as one might have thought.) (2) Recall that lots of the ingredients of Yang-Mills theory are a highly redundant way of describing physics. The gauge invariant stuff we observe in the real world couldn’t care less about much of the specifics of such a description (gauge transformations, the microscopic fields, and so forth). For certain low-energy issues, some systems that you would have thought had nothing to do with Yang-Mills theory may well have the same class of dynamics as seen in other systems that follow more directly from a Yang-Mills construction.
Yang-Mills theory is just a tool, like everything else. It is a starting point, for writing down some dynamics. We should not be too wedded to every last shred of it though, since sometimes the physics flows to a different place that’s far from the starting point. We’ve got to keep our eyes on the physics.
The idea therefore is that while there was no Lagrangian written down in this story based on the variables you might have thought relevant to describing a bunch of interacting (fermionic) lithium atoms, there’s still something to be learned here, since in this strong coupling regime, the theory of the atomic physics has flowed to the same interacting class of models as the horribly messed-around Yang Mills system has. Aspects of the dynamics of both systems are described by these new string theory geometries.
So what can you compute and compare to experiment? Well recall that one of the rather striking results from the plasma story was a measure of the hydrodynamic quantity the sheer viscosity of the fluid, usually presented as divided by the entropy, [tex]\eta/ S[/tex]. This is the first of many hydrodynamic quantities that can be readily extracted from the stringy computations. The “natural” value extracted from the stringy models at leading order, [tex]1/4\pi[/tex] turned out to match the physically measured values somewhat better than other methods in being strikingly (very strikingly) small compared to expectations. There’s a bit of messiness in that story since it is an extremely difficult procedure to extract the hydrodynamic quantities from the heavy ion collisions. The fun thing here is that there are hydrodynamic quantities to be had here too. Experimentalists can, by probing with lasers for example, squish the system in ways that allow for a relatively direct measurement of things like [tex]\eta/S[/tex], including that very quantity.
The prediction from the geometries of Adams et al is that [tex]\eta/S[/tex] is again naturally very small, [tex]1/4\pi[/tex], and this is in line with results reported by Schafer (see here). Apparently there are more precise measurements to come, and while there is yet to be an official report the numbers, rumours are that they are is in line with the stringy predictions, which is rather exciting. A lot more to come, I am sure, as there’s a host of things to compute on one side, and to measure on the other. Who knows how far this will go, and what the range of validity will turn out to be. One to watch.
More strong coupling fun, using duality.