Exploring QCD in Cambridge

exploring qcd sign

So the conference here at the Newton Institute in Cambridge is simply marvellous. I’m so glad I came, and so happy that I was invited to attend and make a contribution to it by giving a talk and having discussions. It’s a rather splendid combination of experimentalists, phenomenologists, and various hardcore theorists of various sorts, and there are ideas just flying around and bouncing off the walls. The title is “Exploring QCD: Deconfinement, Extreme Environments and Holography”, (it’s organized by Nick Evans, Simon Hands, and Mike Teper) and the focus is very much the fascinating nuclear physics of heavy ion collisions at the RHIC experiment at Brookhaven, and the experiments to come on heavy ion collisions at the LHC at CERN. The latter is an aspect of the physics to be done at the LHC that you don’t hear about much because it is sidestepped in favour of discussions about the Higgs, origin of mass, supersymmetry, theories of everything – such as strings, microscopic black holes, extra dimensions and all that other good stuff. (See earlier discussions here, here and here.)

Well, the great thing is that there’s been plenty of discussion of black holes, extra dimensions, strings, and so forth at the conference because of a great deal of promise of its relevance to nuclear physics. It’s been right alongside the discussion of experimental results, and other theoretical approaches such as work on computer simulations of aspects of QCD (“lattice QCD”) and studies involving other techniques. There’s very much a spirit of open-minded exchange among all the various parties involved, learning from each other and all with eyes focused on the main goal: understanding what is now firmly established in most people’s minds as a new -and somewhat unexpected- phase of matter that has been showing up in these experiments. There’s be video of the talks on the Newton Institute’s website soon, and I’ll point to them when they’re up. [Update: Actually, they’re up. I was looking in the wrong place. One of the (excellent) staff at the Institute -those people who do the hard work of making everything run so smoothly and seamlessly- told me today. You can find the talks here, and more are being added regularly.]

The sad thing is (as I’ve pointed out many times before – for example in various seemingly pointless discussions with the largely ill-informed and misleading anti-string spokespeople last year, see e.g. here and here) that this is truly exciting physics where people from so many different approaches and persuasions are coming together in the spirit of getting insights into an exciting new physics problem – and you most likely won’t read about this conference in the press, because it is just not considered news to cover arguably one of the most exciting aspects of doing science – those times when good and useful ideas come from many, varied and sometimes unexpected directions. There’s fewer bitter conflicts and controversies at times like this you see, and more in the way of cooperation and open-mindedness (though still no shortage of lively argument, of course). All not, sad to say, considered urgent things to cover in a science story, even though most good science operates in this mode. Oh well.

So what is the physics? Well, QCD – Quantum Chromodynamics – a kind of quantum field theory, is part of the Standard Model of particle physics, and does a great job of explaining how nuclear matter – quarks and gluons – works in some regimes. This is largely the regime of high energy density and low population density. From this we know about the constituents of the protons and neutrons that live at the core of atoms (and all their myriad cousins that can be observed) – they are made of “quarks” that interact by the exchange of particles called” gluons”, and that’s that.

But things get very tricky when the quarks and gluons are interacting at lower energies, such as the state we’re in during everyday physics – they are locked inside the protons and neutrons, and behave very differently from the high energy behaviour we coax them to do in collider experiments. Furthermore, when you arrange to crunch a huge amount of them together (by colliding heavy ions) so that they are at high temperature and high density, their behaviour is so radically different from the more traditional particle physics regime that nobody knew what to expect, except to say that it would likely be an entirely new phase of matter formed from a sort of plasma of QCD-stuff… People were not even sure whether it should be thought of as a plasma of quarks and gluons in any useful way, in the same way that it is clear that for many things of importance for its properties, describing water as a collection of oxygen and hydrogen atoms is not always the best way to go. The effective description afforded by hydrodynamics is a better bet to come to grips with all the flowing and sloshing around that water can do.

Well, in some sense people were reasonably sure for a while about some things they might see, and one of the points of the discussions in recent years has been that a lot of the expectations were wrong. There was a surprise, coming from the experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven in Long Island. First and foremost, much of the intuition people had gained about QCD led them to believe that the physics they would see at RHIC – when they actually made the quark-gluon plasma (QGP) – would be consistent with the QGP being a nearly ideal gas. A gas in the sense that the constituents would be weakly coupled to each other, with all the resulting properties that entails. It is now looking increasingly likely that this is simply wrong. The QGP (at least the phase of it seen at RHIC) is apparently behaving like a liquid, but a very strange liquid, in that it has unusual transport properties. One of the most striking of these is that is has a spectacularly low (shear) viscosity. (Ed Shuryak gave us an excellent summary talk on this to kick off the conference. Here’s a review talk on the same subject from a few years ago.) Another feature that was unexpected (if you work with the gas idea) was the fact that QCD “jets” (showers of particles that are well known from other areas of QCD physics where the energy in a collision is deposited in a tightly collimated spray of cascading particles) are spectacularly more highly suppressed or “quenched” in the QGP than had been expected.

krishna rajagopal

(Click for larger. MIT nuclear theorist Krishna Rajagopal giving a talk about jet quenching, meson physics, and his use of string theory techniques to study them.)

The quest then has been to understand two things, given that the QGP has turned out to be a strongly coupled QGP, or “sQGP” as it is sometimes denoted now. Why the original expectations were wrong, on the one hand, and what methods and ideas can we find as a community in order describe and understand the physics correctly, on the other hand. This is where the fun really starts, of course, and this is what the conference has been about. (Later experimental studies of the QGP, such as at the LHC, may well show that it has a more gas-like phase at higher temperature, perhaps, but the goal now is to understand what has been seen so far, which is a rather unexpected phase.)

The fun at these times is to find new ideas and techniques wherever you can to help get the job done. QCD as it stands (as a high energy perturbative theory that is) is not really up to the job. The traditional field theory techniques are really geared up to study quarks and gluons in that high energy and low density phase, and not this messy goop. There’s been lots of good work – that is still on-going – using a number of other approaches (primarily lattice QCD), but I’m going to tell you about some of the things that have been happening via the intersection with my field. One the marvellous things that has transpired is that many of us over in the string theory community have been studying -it turns out- just the right sorts of things. Basically, we’ve learned that there are physical regimes where just the class of field theory that QCD belongs to (“gauge theories”) are best described not as four dimensional string theories but in terms of the full machinery that you hear a lot about in the string theory context – extra dimensions, gravity, black holes, and so forth, even though you might have thought those were just not relevant to good old nuclear physics in four dimensions. But that’s one of the wonderful things about doing science, and pragmatically seeking ideas that can be put to useful work.

So there’s been some unexpected connections between these nuclear physics matters and all of that wonderful stuff we’ve been working on. Well, not unexpected to some, I should say. I’m not the only one who’d been anticipating -or better, hoping for- such a fairly direct connection, of course, but I’m pleased to see all this phasesdialogue and activity because I’d been trying to get the community to take this all more seriously since the work I did (with Chamblin, Emparan and Myers – see e.g. here) on the thermodynamic phase structure of these theories back in 1998 and 1999 (largely through various seminars I gave to try to bring out the key idea (see below), and also in my book that came out in 2002).

So it seems like it’s all coming together, although I should say that it was not because people listened to me and took my word for it, but because of some really nice papers that came out (for example, the Kovtun, Son, and Starinets paper of 2004 – part of a longer series of works that included the Policastro, Son, Starinets 2001 paper) that really drove home that the strongly coupled plasmas we are studying with these apparently arcane string methods are of precisely the extraordinarily low viscosity variety. There’s since been several nice papers showing how naturally one can extract a high degree of jet quenching from these models too (see e.g. this one), as well as other interesting and relevant features. (There’s a nice-looking recent review by Makoto Natsuume that I noticed recently that may be of use. Also, that review talk by Edward Shuryak (and others like it) that I pointed to earlier is likely useful.)

ofer aharony talk

(Click for larger. Weizmann Institute string/field theorist Ofer Aharony giving a talk summarizing aspects of string theory techniques for a mixed audience.)

What’s the big idea? Well, there’s a lot to say. The key thing is really that a large number of interesting field theories (in four dimensions, say, but there are other examples too) are well understood to have their physics described by doing string theory in certain ten dimensional spacetime. The prototype of all of this is what is called the AdS/CFT correspondence (which was formulated in three key papers by Maldacena, Witten (here and here), and Gubser, Klebanov and Polyakov – there’s an excellent review here), where the field theory is four dimensional [tex]{\cal N}=4[/tex] supersymmetric [tex]SU(N)[/tex] gauge theory, where [tex]N[/tex] is large. ([tex]SU(N)[/tex] is a sort of symmetry group called a Lie group. [tex]SU(2)[/tex] is a key example in lots of physics, being connected to rotations in three spatial dimensions; the group is not being used like a spatial rotation in this context, however.) The physics of this field theory is captured by doing string theory in a ten dimensional spacetime which is actually in two five dimensional factors: [tex]{\rm AdS}_5\times S^5[/tex] where the first part is anti-deSitter spacetime (a constant curvature space with negative cosmological constant) and the second is a five-dimensional sphere. The radius of each of these spaces is set by the Yang-Mills coupling strength, the tension of the string, and the parameter [tex]N[/tex]. It is the need to allow computations to be done on the string side (largely working in the limit where radii are large and hence curvatures are low), that requires us to have [tex]N[/tex] large.

ads sphere

(Random semi-technical slide from my recent talk, as decoration)

The key thing is that we get to study the full string theory in this spacetime, notably including quantum mechanical gravity processes, and these tell us about the physics of the strongly coupled gauge theory (which has no gravity!), at large [tex]N[/tex]. There’s much more understood about what are generally called “gauge/gravity duals” than just AdS/CFT, but it’s a good starting point for discussion and it is remarkable how quickly one can extract apparently relevant physics from playing with this example. A number of immediate apparent obstacles are maybe not obstacles at all. For a start, QCD is an SU(3) gauge theory, so [tex]N=3[/tex], so it’s not “large” in the usual sense. Moreover, QCD is not supersymmetric and it has extra degrees of freedom corresponding to the quarks, while the string model in question seems to be talking about a supersymmetric theory with the wrong extra degrees of freedom (certain extra scalars and fermions that are no quark-like in many ways) but despite all this, it seems that we can still learn things that are relevant to QCD – and those real experiments, by starting here.

ads cft slide

(Random semi-technical slide from my recent talk, as decoration)

A key point is universality. (A point that I’ve been trying to emphasize for years, although the language is much better these days, and it’s all bolstered by the hard work that many have done to bring out lots of useful examples). Right at the outset, the extra symmetries the model gauge theory has that we know are not there (supersymmetry and another one called conformal invariance) are broken when one heats it up in order to form the plasma. The plasma is then strongly coupled, and it is observed to have a low viscosity and other nice properties. The key universality idea then kicks in: Perhaps there are universal properties of these sorts of plasmas that can be extracted from these string theory techniques. The hope is that the QCD plasma is in this same universality class and so we can learn how to describe some aspects of these experiments from these studies. (We know a lot about the phase structure of solids, liquids and gases like ice, water, and steam – and how to move between them – by studying simpler models that have phase structures have the same universal behaviour (in the “same universality class”), rather than by studying all the details of combinations of lots of hydrogen and oxygen molecules, which is hard to do).

dbranesThat connection would of course be marvellous, not the least because the hot plasma is modelled by the physics of black holes in the AdS spacetime! This is both fun and gets at a key point about why the universality might arise and be credible. Black holes are rather simple and special things in that they are known to have many universal aspects of their physics – all boiling down to the fact that an event horizon (that famous point of no return) forms, regardless of what the hole was originally made from, and event horizons come in very few sorts – and so since the gauge/gravity duality technology tells us that the thermal physics of these plasmas seem to be related to a black hole in whatever the gravity dual spacetime of that plasma happens to be, the universality of the black hole physics translates into the university of lots of properties of the plasma, including lots of transport phenomena (like viscosity) which are hard to extract from other QCD techniques. Even if it turns out that we cannot construct a controllable gravity dual to QCD itself, the universality idea would say that the thermal transport properties of the plasma would be captured by a black hole in that (hard to access) gravity dual, and is thus related to the simpler plasmas that we can study more easily. (An obvious escape clause here is the possibility that QCD does not have a gravity dual and so escapes the universality argument in this manner. That remains to be seen.)

So the idea is that these techniques can probably sit alongside (not replace) the other techniques being used to study these new regimes of physics (at least this sQGP phase, if not other phases of the plasma that may well be discovered), and, as a nice by-product, we’ve found a rather cool application for those “crazy” things like extra dimensions, quantum black holes, and quantum gravity, which most people thought were simply not relevant to the real world (at least not in this way, if at all).

There’s a lot to do, and the jury is still out on just how far this will go, but it is already fair to say that there has been a fruitful flow of ideas already. Who knows just how much more we’ll get from this approach and these cross-pollinations?


(See also an earlier post from last year by Bee and Stefan on aspects of this topic.)

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25 Responses to Exploring QCD in Cambridge

  1. Steve says:

    Aaaah! QCD in Cambridge. Humour me and let me reminisce. That takes me back to my PhD years at the Cavendish Laboratory around 1980, doing higher twist QCD calculations by commuting loads of operators around until the expressions were separated into various canonical pieces. Even back then I knew it had to be more efficient to use an algebraic manipulator, but somehow I thought it was safer to do it by hand. I left QCD to do information processing research (and I’m still doing that). Amazingly, the same sorts of operator manipulation that I did in QCD have turned up recently in my research on information processing using discrete symbols (quanta, if you wish). This is a bizarre example of coming full circle!

  2. Clifford says:

    Yes, one never knows what may turn out to be useful in unexpected places.


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  4. Blake Stacey says:

    Having first seen “universality” in the statistical physics of things like gases and magnets and Ising models, I get a great kick out of seeing the same notion in string theory!

  5. Clifford says:


    Actually we use it all the time, especially exactly the same notions from statistical physics. In fact, most of the traditional formulation of string theory itself is based upon conformal field theories (in a certain gauge, consistency tells you that the background in which the string is propagating is consistent if you have a conformal field theory)… and you’ve met those theories before yourself, probably… they exist precisely at transition points in various statistical models, where the universal physics lives. This is one of the really nice things about this field, it gets one to learn a whole lot of physics from all sorts of wonderful sources… and field theory and stat mech and all that good stuff are such fundamental concepts in doing string theory.



  6. pedant says:


    Now that you have come full circle, do you still do it ‘by hand’, or surrender the greater part of the toil to a deus ex machina like Maple? And is the assistance provided by computer algebra widespread in string and other theories these days?

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  8. Steve says:

    Nowadays I call upon the services of my trusty companion Mathematica to do all the heavy lifting. I have been a Mathematica user since before version 1 when it was known simply as SMP (symbolic manipulation program), and we now live in symbiotic harmony where (my copy of) Mathematica and I need each other to just get through the day. Of course, I occasionally get the urge to do it “by hand” as you so coyly put it, but the experience is frustrating and is a pale shadow of the real thing! As for the use of Mathematica (and the like) in string theory, I don’t know the answer because I don’t do strings myself, but it seems that “manual studies” are the method of choice for a small but vocal minority of string theorists…

  9. Clifford says:


    The use of Mathematica, Maple, and other such packages along side the usual techniques (pen and paper and so forth) is quite routine in lots of areas of physics research now. They are especially useful for automating a long and tedious computation that you might have done the first time by hand to get right, but then want to run several times with different starting points, etc. You change the first line, run it again at the click of a button. Also, their use has allowed tedious computations that would take years of chugging away to be done in very short times, allowing amazing strides to be made in many areas of research.

    Make no mistake… they are not a substitute for thinking. you have to know what your doing or you’ll just get garbage out for the garbage put in. Yes, that is still true, and always will be.



  10. Aleksey Cherman says:

    Dear Clifford,
    The attempt to make use of AdS/CFT methods to understand strongly coupled systems like the sQGP is really, really cool mathematical physics.

    I’ve a couple of questions about the universality class argument that is given to support applying the stringy results to QCD (and other strongly-coupled systems, as other people have tried to do.) I’ve previously thought that in the statistical mechanics context, systems in the same universality class have the same critical exponents – but do not necessarily share other properties. Why would one expect transport coeffiecients to match? Is this wrong?

    I am also curious just how wide this universality class that (might) include supersymmetric field theories with gravity duals and QCD should be taken to be. For instance, it’s been shown by Kovtun, Son, and Starinets and others that \eta/s >= 1/4\pi in a certain class of field theories with gravity duals, with the bound being saturated when the ‘t Hooft coupling is infinite. This has then been conjectured to be true more broadly (that is, that the bound is ‘universal’). That is, it’s been conjectured that this bound born in a stringy context applies to _all_ fluids, or perhaps just those described by sensible quantum field theories. (This would include the sQGP that’s produced at RHIC.)

    This would be extremely exciting if it were true, but at least in some cases (hep-th/0702136) it is possible to construct (contrived) counter-example systems that violate the bound by essentially having a large entropy s. So it’s not clear in what _precise_ sense such a bound is universal – that is, it’s not clear to what the bound might apply outside of the setting where it was derived.

    As a disclaimer, Tom Cohen, whose paper I cited above, is my advisor here at UMD, and we just finished a paper on this issue.

    Aleksey Cherman

  11. Clifford says:


    I think that these are all interesting questions that nobody has answers to yet. There is an exciting feeling of adventure here…. people are experimenting with many examples, and patterns are beginning to emerge. I suspect that a whole new definition of “universality” will apply here – not the one relevant in critical phenomena. I wish I had more answers, but on the other hand, I don’t think anyone does.

    I honestly don’t know what to think about the contrived counterexamples to the proposed bound of Kovtun et al. Do the examples preserve unitarity, by the way? I’ve not read the papers to really have a good handle on this – is this equivalent to an extraordinarily large number of species?

    Sorry to be not so useful…



  12. Aleksey Cherman says:

    Hi Clifford,
    The contrived counter-examples preserve unitarity.

    They are equivalent to having a very large number of species. In some of the counter-examples, there are explicitly a very large number of species, while in another variant there is a rather weird inter-particle potential that has the effect of producing a very large entropy by allowing a very large number of very long-lived resonant states.

    This line of work by the string community (and others) is very very exciting, and really cool mathematical physics, and I hope the quantitative nature of the universality of the results will be better understood soon!


  13. Clifford says:

    I hope so too. In the meantime, it’s already been instructive, and a lot of fun.



    P.S. There might have been some discussion of the species issue in Starinets’ talk at the conference… in response to a question… I do not know if the microphones picked up the discussion, but it is worth listening to find out. If you can decipher the content of the discussion (which I admit that I do not recall), feel free to come back here and mention what you found. Might be a good launching point for ideas or discussion.

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  17. Kaila Yu says:

    Hello…I Googled for learn chinese language, but found your page about ring QCD in Cambridge – Asymptotia…and have to say thanks. nice read.

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  21. Yoron says:

    Hi, I really like this approach to the vacuum. The reason why I have ambiguous feelings towards the idea of strings are their, as I understands it, one dimensional approach. That seems to open it to new questions about how they are thought to ‘glue’ themselves together, introducing new ‘interfaces’ that also will need to be explained?

    But I’m starting to think of dimensions in terms of ‘properties’ instead. Would that make any sense to a string theorist, or would that just be heresy?

    As if what we have in our ‘expansion’ for example would be 3D-points introduced ‘instantly’, whole in themselves, no ‘glue’ needed. And as I see it, still allowing for different ‘dimensionality’s’ in themselves, but if proved to be f.ex 11 then being exactly that, even if we see only three of them and times arrow of course.

    It would solve this glue-problem that I get stuck on trying to imagine them, much in the same way we describe a photons ‘spin/polarizations’ and masslessness etc.

    Or do string theory need to set each dimension as a ‘force’ of it own to make sense mathematically?

    I mean, I really like the ‘liquid’ picture.
    all that ‘fizzling’ going on ::))


  22. Yoron says:

    Hmm, meant ‘fizzing’ there..
    Shouldn’t trust my word compiler that much huh 🙂
    Any way, hope it made some sense.

    Cheers again

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