Friday, April 21, 2006

Why the Quark Gluon Plasma is a Banana

When I was in 5th grade, our biology teacher dropped out for a longer period. For whatever reasons, she was temporarily replaced by our maths teacher. He was about to be retired soon, and had not taught biology for more than 20 years. Now he saw himself faced with the task of giving "sexual education" to a bunch of 11 year olds.

After having extensively discussed various forms of STDs, we all were completely sure we would never ever have sex in our life. Our teacher then proceeded to safe sex, and eventually produced a banana to explain the proper use of a condom. He was clearly struggling with words he hardly ever used in his life, and the banana seemed to us a very theoretical example for a very involved practical situation.

I thought about this banana, when I was in very interesting seminar at the KITP last week by Pavel Kovtun, titled

How Can AdS/CFT Be Useful for Heavy Ion Physics?

There, in this seminar room, all the stringy guys were talking about jet suppression, shear viscosity and central collisions! It was equally weird as hearing your maths teacher talk about sex.

In the talk, it was explained how the AdS/CFT correspondence can be used to model certain properties of heavy ion collisions. I find this an interesting topic, with a clear connection to phenomenology, which I often miss in talks at the KITP.

It also reminded me of a colloquium by Joe Polchinski that I heard about 3 years ago at LBNL. The only thing I can recall was that he said something like the quark gluon plasma is a black hole. He most likely said more, but I was too nervous to listen, since own seminar (the first seminar I ever gave outside my home institution) was scheduled for the following lunch meeting. Consequently, the only thing that was in my head while I was giving my seminar (which btw had nothing to do neither with heavy ions nor with black holes or qcd) was what the fu*k a black hole has to do with the quark gluon plasma, and why I ever agreed to give this seminar.

Had someone told me at this point that I would end up at UCSB three years later, no way I would have believed it.

1. AdS/CFT

So, here are the rough basics that I hope are sufficient to get into the spirit. Strongly coupled QCD is messy soup, and calculations are nasty. It turns out however, that above the critical temperature, a conformal field theory is a pretty good description of the messy soup (see slide 8 of talk or picture below). Plotted is the energy density (epsilon), normalized to that of a Stefan-Bolzmann gas (subscript SB). The colored curves are lattice calculations, the black line is a conformal field theory - the maximally supersymmetric yang mills theory, which comes with two parameters: the coupling constant g, and the number N of the gauge group SU(N).

So it seems, instead of QCD at finite temperature, it's a reasonable try to model some properties of the mess with a conformal theory, like the mentioned super yang mills theory (SYM).

That by itself does not make things less messy, but now one uses the AdS/CFT correspondence! And here, the miracle happens: the 4-dimensional SYM gets translated into 5-dimensional gravity in some space called AdS5 x S5 . Which is much easier to deal with.

One can then translate quantities from the 4-dimensional field theory into the 5-dimensional gravity in this specific space. E.g. the

The stress-energy tensor in SYM translates to a graviton on AdS5 x S5

A state in the field theory translates to a state in the dual geometry

An operator in field theory translates to a field in the dual geometry

Etc. if you want to specify the type of particles you are looking at (fermions, gauge fields), things get more complicated, but are doable. Most importantly

The thermal equilibrium state in SYM translates to a black hole in AdS5 x S5

And so, Marcus, I am very proud to say that at least my time at UCSB enabled me to answer the question what the QGP has to do with a black hole.

However, the general relativity one has now translated the field theory into, is classical only for large N. For small N, one would need to know quantum gravity - or string theory. It is usually assumed that N is 'large enough', which might or might not include N=3.

2. Applications

Using the above translation, one can now examine observables. A prominent example is e.g. the shear viscosity and it's lower bound. But also the photon and dilepton emission rate, or the energy loss of particles traveling through the messy soup can be investigated. Besides Pavel's talk, you might want to check some of his papers. It seems to me, he is working on an enormous amount of related stuff. Some more references about the topic

3. Problems

There are most likely a whole number of theoretical, analytical and numerical problems with the approach that I am not aware of, and therefore will not mention. Starting from the question whether N=3 is indeed a large number, or the assumption of thermal equilibrium, I have the vague impression there are more subtleties than I can (or want to) imagine.

Still, I think it's a reasonable try to use AdS/CFT for SYM to model properties of heavy ion collisions. Instead of, say, some hydrodynamical description, un-quantized numerical models, or cost- and time consuming lattice calculations.

The biggest problem I have with the scenario is the formation and time evolution of the fireball. Thermal equilibrium might correspond to a black hole in the dual theory, but what describes the collision, or the following hadronization?

The intention to use often very abstract mathematical theorems for direct applications is definitely something I welcome, esp. since the front research in theoretical physics is falling more and more apart into sub-fields.

It requires quite some courage to go to a heavy ion conference as a string-theorist, something Pavel did last month, which really surprised me. I am not sure though whether the average heavy ion physicist would already consider the approach to be more than a theoretical example for a practically very involved situation.

To come back to the banana issue: I am very relieved to tell you that I, and most of my classmates, eventually recovered from my maths teacher's lectures. We all figured out how to properly use a banana.

Acknowledgements: I would like to thank Pavel for his patience with my questions, and I apologize for the banana. I could not resist the temptation.


  1. Dear Bee,

    thank you a lot for this very interesting post and all the references and links you have collected! This is a topic I would like to know more about, and I will try to follow up some of the papers you have mentioned. It is funny to see that the abstract reasoning about black holes in anti-de Sitter space seems to have some relevance for down-to-earth heavy ion physics!

    I have first heard about this at last Strange Quark Matter, in a talk of Laszlo Csernai where the Kovtun-Son-Starinets viscosity paper is mentioned. Hearing about anti de Sitter space in a heavy ion conference is probably as strange as listening to string theorists talking about elliptic flow ;-).

    It's really worth listening to the straem of Pavel's talk, especially for the discussions in between. By chance, I had a dicussion with Ben and Stefan StrĂ¼ber on Friday over coffee after lunch about this topic. I guess they can find answers to some questions we couldn't solve in this lecture and in Pavels talk in the Winter Workshop on Nuclear Dynamics. I must admit that I didn't know that an ideal gas has not zero, but infinite viscosity.

    By the way, what exactly does this N stand for in the N=4 Supersymmetric Yang-Mills? I understand it is neither the number of colours nor the number of flavours, but what then? And there is a discussion about N=1 at some point, what does this mean? And the "large N" limit mentioned, that relates, as usual, to the number of colours?

    So, the imporant thing is that this N=4 SYM is conformal, because then, there is a relation to black holes in AdS? But then, I do not understand: QCD has a mass scale, this Lambda_QCD or whatever. How goes this together? Does this mean that the theory just works in the temperature range where this energy density scaled to Stefan-Boltzmann is roughly constant? What happens when the coupling constant changes smoothly? Is there a corresponding change in some parameter of the CFT? And that e/e_SB is nearly the same for 2+1 flavour LQCD and N=4 SYM, is that a coincidence? The particle content of both theories is very different, right?

    The argument that the observed data of the elliptic flow imply a very low viscosity, is, I think, not that clear yet, since the initial conditions asumed for the hydrodynamics are quite important. For example, also just last Friday, Yasushi Nara told us in the palaver that an initial state calculated from the colour glass condensate picture and evolved with non-viscous hydro overpredicts elliptic flow. There, maybe, assuming a higher viscosity could help to fit the data. So I am not sure that one can say for sure that the viscosity of the QGP in a heavy ion collision is really that low. Probably EuroGirl can tell us more about this...

    All the best,

  2. in "N=4 super Yang-Mills", N counts the amount of supersymmetry. minimal susy has N=1, that is one conserved charge which is a Lorentz spinor. large-N limit in AdS/CFT refers to the usual number of colors for SU(N).
    conformal invariance of N=4 SYM is not essential for AdS/CFT to work: there are other non-conformal field theories whose dual description involves black holes in AdS. it's just that N=4 SYM is the simplest one to study. there are N=2 and N=1 examples in AdS/CFT which describe non-conformal field theories with discrete spectra.

  3. Hi Stefan,

    for whatever reasons the viscosity issue always confuses people. Here is how I understand it: viscosity is the ability of a fluid to drag along layers while flowing. A large viscosity means the fluid does not easily drag along layers. It does not flow that easily and is 'thick', like honey or so.

    On the other hand, a strong coupling in the medium allows to drag along layers very good. Thus, a strong coupling corresponds to a small viscosity, whereas a small coupling corresponds to a large viscosity.



  4. Hi pavel, and bee,

    thank you for these quick answers from SB :-)
    I guess I will have to look up some elementary SUSY stuff, to understand these possible particle contents for the different N's...

    So, in this AdS/CFT correspondence, the conformality of the QFT is not so important? The big thing is that the 3+1d QFT is defined on some boundary of the AdS, and that the theories on the boundary and in the AdS bulk are related? Ok, I see, that's then why in hep-ph/0501128 they talk about a Holographic Model of Hadrons. Mikhail Stephanov gave a talk about this paper here in Frankfurt some months ago, but unfortunately, I didn't understand too much of it then.

    This thing about viscosity, I still don't get it completely. What I had in mind: Think of that undergraduate lab experiment where you drop a small solid sphere in a cylinder of a fluid and measure the Stokes drag. From the stationary velocity of the fall, you can extract the viscosity, and there, the slower the fall, the higher the viscosity. Now, thinking about the sphere falling in an ideal gas, naively I would expect a very low viscosity, not an infinite one. I mean, the sphere is not supended in the air, after all ;-)... So, I will have to think about this once more...

    BTW, Laszlo had on slide 23 of his SQM talk a nice illustration about how a minimum in viscosity can occur when going from a dense fluid to a dilute, non-interacting gas by focussing on the mean free path:

    In the dense liquid, there is a large mean free parth of "holes", while in the dilute gas, the particle mean free path is high. In between, there is a minimal mean free path, corresponding to a minimum of the viscosity. I guess I start to understand ;-)...

    Best, Stefan.

  5. BTW, I just have seen - there is a feature article about the quark-gluon plasma and the RHIC experimental results in the may issue of the Scientific American, The First Few Microseconds, by Michael Riordan and William A. Zajc. Zajc is the spokesman of the PHENIX experiment at RHIC. The AdS/CFT thing and the issue of viscosity are mentioned on page 4...

    Best, Stefan.

  6. Dear Bee:

    Congratulations on your wedding. I suppose you'll be on your honeymoon and won't get this for a while. Hope you're not too 'changed' to reply back!

    It's interesting that the QGC can be equated to a mini black hole. Of course, that is essentially what Hawking's theory of evaporating mini black holes implies.

    Way back when (1999) I wrote a brief letter to Scientific American, which they were kind enough to publish, in which I theorized that mini black holes could be created at the RHIC, the LHC, etc. if the colliding atoms were of sufficient energy. However, using Hawking's formula for the lifetime of such black holes, I calculated that they would evaporate on the order of 1E-40 seconds (I don't have my exact figures in front of me right now)

    That is so short, that any such black hole would disappear before it could travel even the diameter of a proton, traveling at the speed of light. Hence, I concluded that it would be safe to make such particles (i.e. no doomsday scenario). However, not wanting to rely on my calculations alone, I wrote to SA expressing the above views.

    Surprisingly, they also published a letter from Frank Wilczek, who stated I was absurd to suggest that mini black holes could be created, but he postulated that Strangelets could be, but not to worry, they could not grow.

    Now, it's being theorized that I was indeed correct, using the latest empirical evidence at the RHIC, in which theorists have asserted that mini black holes (along the lines of the QGC = mini-black-hole scenario you describe) are possibly being produced at RHIC, but that they rapidly evaporate, exactly as I had predicted might be possible in that 1999 Scientifc American Letters to the Editor.

    I have also since investigated Strangelets, and find them more troubling than mini black holes.

    Stranglets are predicted to be a more stable form of nuclear matter, and would accrete normal nuclear matter to them, which would be a more stable state. Many experiments have been done looking for strangelets.

    They too are predicted to be radioactive (i.e. decay back into normal matter) if they remain small and do not grow.

    What is troubling is that their stable state may be sufficient that they overcome the Coulomb barrier that would normally keep positive nuclei (of nearby normal matter) from coming too close (if they too are postively charged, which is what keeps, for example, two positively charged deuterium nuclei from fusing into Helium, which because of the net energy release, is a more stable state than two deuterium nuclei sitting side by side).

    Actually, that's not quite true. Deuterium nuclei do spontaneously fuse with each other, but at a very low rate (i.e. ca 1 fusion/1E23 seconds per deuterium pair). The covalent bonding distance between the two is just barely close enough to get, for example, about one fusion per second in a liter of deuterated water (heavy water).

    Steven Jones in the 1980s at BYU did DOE funded experiments in which he introduced muons into deuterated water, and dramatically increased the spontaneous fusion rate. Apparently, the muons, being much heavier than electrons, shortened the covalent bonding distance (after substituting in for the electrons) sufficiently that the nuclei, now being closer together, allowed for more 'overlap' of the strong nuclear force, causing a dramatic increase in the spontaneous fusion rate (ca 130 fusions/introduced muon!).

    What we really don't know is how much stronger the nuclear fusion potential for a small strangelet would be, for example, compared to that of the fusion potential of deuterium. I.e., would they spontaneously fuse at an appreciable rate, even if kept away from normal nuclei at a distance of the covalent bond distance of Hydrogen?

    The cosmic ray argument is pointless.

    Cosmic rays produce fast moving particles when they strike a stationary particle, and high E cosmic rays (i.e. 1E17 and up) that mimic the RHIC, LHC, etc. would produce a strangelet moving at very high energy at nearly the speed of light relative to the planet they strike; a considerable contrast to ones produced in a laboratory, at relative rest to the laboratory, where there is a an environment rich in low-Z atoms (Hydrogen in the plastics, Helium in the coolants for the superconducting magnets, etc.)

    We know, by empircal testing, that fast moving neutrons behave entirely differently than slow moving neutrons; would the same be true for strangelets?

    Anyway, since Franck Wilczek now appears to have been wrong in his criticism of my suggestion that mini black holes might be produced at the RHIC/LHC, might he also be wrong about his prediction that strangelets would be 'safe' if they were produced?

    My calculations show that any one such strangelet would actually 'grow' quite slowly at first, taking perhaps millions to billions of years to weigh one gram. That is because the fusion would not be exponential (like in an A-bomb) but rather very nearly linear at first) However, if we inadvertently produced millions of such strangelets, it would then become a problem.

    Anyway, food for thought, and perhaps we'll have a chance to meet, as I live in Hawaii, but have an office in Monterey, California as well.

    Best regards,

    Walter L. Wagner (Dr.)

  7. Dear Dr. Walter L. Wagner,

    Study of potentially dangerous events during heavy-ion collisions at the LHC: Report of the LHC Safety Study Group

    See Chapter 2. Strangelets.

    Sorry for the brief answer. Have to go get married now ;-) Best,


  8. Thanks for the quick response.

    Already read that. It's patterned after the one they did at the RHIC.

    They overlook many things, but I'll let you go get married, and we can go over it after you get back.

    Here's a philosophical question, though. If it were possible to calculate the 'risk' associated with creating a 'deadly strangelet', etc., and it came out to be exacly 1/1,000,000,000 (one in a billion), can we justify doing such experiment?



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