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Heavy ion physics and AdS/QCD

The Lagrangian of QCD has been written down more than 30 years ago and I think it is fair that say that we have known that it is the correct fundamental description of the strong interactions which includes nuclear physics and heavy ion physics, among other subfields, for many decades. Even the Nobel prize committee has agreed with this assertion for more than two years.

From the viewpoint of a complete idealized theorist, the main questions about the strong interactions have been settled for a very long time. And it has been a good idea for these theorists to re-focus on new physics at shorter distance scales.

But physics is not just about the fundamental Lagrangians as some of the idealized theorists could think. It is about the understanding of all possible phenomena and about predicting of the outcomes of experiments in a wide variety of physical situations. What did the people have to do in order to get a better grasp of nuclear physics, heavy ion physics, and similar "messy" fields that exhibit complex behavior whose essence is captured by QCD?

Well, people had to perform a lot of experiments, find phenomenological laws, and justify these laws from the fundamental equations. The physicists had to think about a plethora of possible new approximations, concepts, and ideas how to visualize what's going on in a more accessible way.

Some of these ideas look like a systematic - and in principle, arbitrarily accurate - mathematical treatment of the fundamental QCD Lagrangian: perturbative QCD and chiral perturbation theory. Others don't. People had to design models with new emergent objects that some of them could see in the mess and they had to think about new phases in the QCD phase diagram. The quark bag model and the color glass condensate are examples.


The most far-reaching new technique in the research of strongly coupled gauge theories is undoubtedly the AdS/CFT correspondence. The previous sentence doesn't mean that the AdS/CFT correspondence has suddenly become the only tool to be used in nuclear physics or heavy ion physics. But it does mean that many people have very good reasons to expect that this tool will be the most efficient one to understand questions about the strong force that have been difficult to understand with the previous tools.

Most of the 5,000 or so followups of Maldacena's original paper deal with the N=4 supersymmetric gauge theory in four dimensions. This theory has many theoretical advantages: the maximal amount of supersymmetry constrains its dynamics in such a powerful way that we not only know the exact Lagrangian of the boundary CFT but we also pretty much know how to expand the physics around the opposite point, using the bulk AdS description.

This N=4 theory exhibits S-duality - that is important not only for the Langlands program - and it has many features that allow us to study its properties using some of the simplest backgrounds of string theory. The rules to calculate its on-shell Green's functions using the twistor methods and CSW prescriptions look particularly natural. The theory may even be integrable. I could go on and on and on but the main point is clear: this theory is a priceless theorists' playground.

But it is not just a pure theorist's perspective that makes the N=4 gauge theory important. This theory has many features - qualitative and, in some limits, quantitative - that seem to be universal for all gauge theories or at least all confining or conformal gauge theories. Although a theory that is as fancy as the N=4 theory could have seemed to be an unexpected starting point to study the real world, it is becoming increasingly clear that this theory is a very important zeroth approximation for computing things and understanding of strongly-coupled gauge theories in general.

This relevance of a seemingly abstract theory for the understanding of reality couldn't have been obvious from the beginning. But it seems to be rather well-established today: such a new piece of knowledge is what I personally call progress because it shows which effects and fields are actually relevant for particular observed phenomena rather than to simply confirm someone's pre-conceptions and to fit them with a random phenomenological model. Also, all sensible physicists agree that for theories like the N=4 theory and probably many others, the holographic correspondence is not only true but it is also a very important lesson about the character of gravity and gauge forces in our quantum world.

QCD and holography

With the successes and theoretical depth in mind, it wasn't unexpected that many people started to apply the AdS/CFT methods to the real QCD: this direction of research is called the AdS/QCD correspondence. It is work in progress but it has already led to surprisingly good results. Of course, just like in other approaches, it is not guaranteed that the successes will grow arbitrarily high.

The real QCD doesn't have any supersymmetries: the fermions and scalars in the adjoint representations are missing. On the other hand, the real QCD has quark fields in the fundamental representation. This difference is unimportant for some phenomena - dominated by the pure gauge field sector - and important for other phenomena. Whenever the differences are important, it is usually possible to keep on refining the dual bulk description in order to get more accurate results.

I don't think that the real goal here is to find a completely accurate dual description of QCD: in some sense, I tend to think that the QCD Lagrangian as we know it is the only truly complete and accurate description of QCD physics and the best definition of a dual bulk theory is again the QCD Lagrangian. ;-) But the string theory methods are certainly extremely useful to get a better intuition for many situations and to generate new kinds of expansions: for example, at temperatures higher than "Tc", supersymmetry is broken anyway and the N=4 theory is expected to agree with observable phenomena.

Also, the dual stringy methods based on quantum gravity only become useful and gravity-like in the limit of a large 't Hooft coupling which usually requires a large number of colors N. In QCD, we have N=3 which is pretty close to infinity - in the sense that 1/N = 1/3 is pretty close to zero - which explains why already the first terms in the 1/N expansion gave results that were more encouraging than expected.

Some blog articles about the AdS/QCD program include:

As I have suggested, the AdS/QCD approach can't be expected to end up with a different rigorous form of the QCD Lagrangian because at a finite coupling, the dual bulk theory is not local and the incorporation of all the necessary corrections would make the very definition of the dual theory very complex.

But because the complex and non-local terms are suppressed by a small parameter such as powers of 1/N, the approach can be expected to describe an increasing ensemble of observations with an increasing accuracy. This approach is based on the insight that many theoretical physicists consider to be the most important result of theoretical physics in the last 10 years which makes it clear that the physicists will continue to look at it even if they encounter the first hurdles.

When the dust is settled, I am pretty sure that the description of many situations based on the AdS/QCD will become the favorite one simply because there are many situations in which the stringy behavior of the strong interactions is undeniable. The correct effective degrees of freedom in different regimes are those that are dictated by a careful analysis involving string theory, among other things, and there is no way for an informed physicist to deny this fact.

Many RHIC experimenters as well as theorists are really thrilled by this new framework to study their field. I believe that it is a responsibility of every expert to try to find the most correct answers to the questions that he or she is trying to solve. In this sense, I think that one should expect that the heavy ion theorists will try to learn these new things that have already been successful. If they don't look at it, they are at risk that their field will be taken over by younger colleagues equipped with more modern and up-to-date tools.

It would be counterproductive and silly for the older heavy ion theorists to be throwing artificial hurdles in front of the new researchers in the heavy ion field who are using tools that their older colleagues could have discovered years ago if they had been more creative. It is very entertaining if some of the old, well-known, but more reactionary members of the heavy ion community offer pictures of Pinocchio in their talks - but being entertaining is not necessarily the same thing as having something to say about physics.

Figure 1: "Say it," the blue politically correct official asked Pinocchio. "Sure, why not? The AdS/CFT correspondence is not the most important insight of the last decade about the behavior of strongly coupled gauge theories," Pinocchio said and his nose has exploded as it always does when the poor Pinocchio doesn't say the truth.

If someone is more interested in Pinocchio's awards rather than the fascinating bounds on viscosity or the mean free path that can never decrease below the de Broglie wavelength - the latter fact comes from the Bekenstein bound in the bulk - that are nearly saturated in reality and that can be rigorously calculated from the bulk gravitational theory (and, as far as I know, from nothing else), he may very well become a subject of Witten's anti-fuel policy. And The Reference Frame will leave the detailed discussion of Pinocchio to a Western European physics blog and Asymptotia, websites that apparently think that Pinocchio is more important for QCD than we do. We prefer the picture if anything. ;-)

For a recent technical but accessible talk about AdS/QCD by Pavel Kovtun, see these files:

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reader Leucipo said...

The real QCD doesn't have any supersymmetries: the fermions and scalars in the adjoint representations are missing. On the other hand, the real QCD has quark fields in the fundamental representation

I am not so sure that the real QCD does not have any supersymmetries. The real QCD is the one with 3 colours, not the large N_c limit. And the fact of having N_c=3 creates low energy colourless states for spin 0 and 1/2. Smart labeling of flavours can simulate some supersymmetry, and in fact I remember some articles claiming that the first supersymmetry algebra was introduced in the sixties aiming to classify the hadronic states.

reader Leucipo said...

Hmm, I would stress that even in the N=3 case we need at least 2 flavours to get spin 1/2 baryons. Of course the 1-flavour SU(N) model gets their baryons with a spin N/2, as already remarked in (Witten 1979). And N_f=2 keeps having 1/2 baryons all the way to large N, because the statistics is not very different of the theory of a nuclei with protons and neutrons (also explained by Witten there).

Other point is that in N=3 the symmetry between mesons and hadrons can survive to the introduction of quarks, because in such case a diquark happens to be the same colour charge than an antiquark. As far as I can see, this is lost when considering the high N expansion, isn't it?

Note that the survival procedure includes electric charge in a very pretty predictive way: we neet to set the electric charge of one quark to be -2 times the charge of the another. In this way the charge of a antiquark can be composed from the charge of two quarks. For instance, consider two quarks u, d, and set d=-1/3, u=2/3. The charge of -u is equal the one of the diquark (dd) and the charge of -d is equal to the one of diquark (du). The extant diquark (uu) is not really needed in the phenomenology because (uuu) has spin 3/2.

Of course, you could argue that even if there is a way to rule out (uu) you still want to see the same number of degrees of freedom in (fermionic) quarks than in (scalar) diquarks. I am not sure if there are exotic solutions, but a possible one is to triplicate the number of quarks and, besides to forbid (uu) binding, select one of the u quarks so massive that it does not bind at all. Such ad-hoc measures give you the required 6 diquarks for each value of the electric charge.

As a bonus, if in this ad-hoc replication of quarks you look for uncoloured mesons but allow the (uu) kind of binding (now that it is u anti-u), you get 6 charged +1, 6 charged -1 and, eek, 13 neutrals.

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