Does String Theory explain Heavy Ion Physics?

Earlier this week, we could follow a quite heated debate about the applications of the AdS/CFT (Anti-deSitter/Conformal Field Theory) correspondence to strongly coupled QCD (Quantum Chromo-Dynamics, the theory of quarks and gluons) as observed in relativistic heavy ion collisions.

Or, in a more catchy phrase, whether or not "string theory explains RHIC physics". Or -- even more provoking -- as it was formulated in the recent Nature issue:

"When the Relativistic Heavy Ion Collider at Brookhaven National Laboratory in Upton, New York, first produced a hot quark gas, it was string theory that correctly predicted, retrospectively, some of the gas's properties. "

Nature 443, 491(5 October 2006), Theorists snap over string pieces, by Geoff Brumfiel, see also here.

(Okay, I take the word 'explain' in the title instead of 'predict', but I want to bring that quotation with the alleged prediction somewhere. - If it's unavoidable. - It is.)

This is quite an experimental post written by both of us, trying to understand what is there about these claims. If you ever want to test how much your marriage can take, try to write a blog post together. When you see remarks in brackets, these were the issues we couldn't settle.

In an earlier post, Bee reported on a talk about the applications of AdS/CFT to heavy ion physics that she heard at the KITP. She was thrilled to see string theorists trying to get in touch with experiments! And isn't it ironic that after several decades string theory has come back to where it started from: explaining features of the strong interaction? That was, before it was promoted to be a promising and promising and promising approach to the theory of everything (TOE), which would become important at unobservable energies. (Isn't that too sloppy? - It is called cynicism.)

The use of the AdS/CFT correspondence for strongly coupled QCD is an extremely interesting and exciting project, and probably one of the hottest and densest topics that is currently out there. (haha - sorry, could not resist the temptation) It can provide us with a lot of important insights into QFT. But one should be realistic here:

From the side of the string theorist, realistic about what it can possibly tell us about string theory as a TOE, and what it can't. From the side of the nuclear physicist, what it can possibly tell us about heavy ion collisions. And what it can't.

So, this is an attempt to explain some of the physics involved, from the point of view of relativistic heavy ion physics - and since since Stefan has some background there, we figured we would make a good team, but he's definitely the one to ask what a horizontal flow is. (I should know that by now, but I keep forgetting it. - Does that mean I have to answer all the comments?!)

Here's the outline:

1. What is this all about?
2. Is it a Hype?
3. What does it mean?

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1. What is this all about?

Heavy Ion Collisions have one big goal: To map out the phase diagram of nuclear matter. The question one would like to answer is: Under which conditions of temperature and density is nuclear matter made up of hadrons (of nucleons like neutrons and protons, of hyperons like Sigmas and Lambdas, and so on), and when and how will one find the constituents of hadrons, the quarks and gluons, as the relevant degrees of freedom? Where in this diagram is the phase boundary between the hadron gas and the quark-gluon plasma, as the state where confinement is lifted and quarks and gluons can move freely is called? And moreover, what are the properties (the equation of state, or transport properties such as viscosity) of the quark-gluon plasma?

(Phase diagram here? - Good idea. - Where's the figure from your talk? - Where's yours?)

On the experimental side, there is only one tool available: Accelerate nuclei of heavy atoms such as gold or lead, and let them collide. At the collision, the kinetic energy of the nuclei is dissipated, and goes into the compression and heating of the nucleons in the nuclei. If heating and compression are high enough, a quark gluon plasma can be formed.

On the side of theory, there is QCD which describes the interaction of quarks and gluons. There is only one big problem: QCD is a complicated theory, and its low energy limit, which contains the hadronic ground states, the protons and neutrons and so on, can not be handled analytically. The same is true for the deconfinement transition from the hadronic world to the quark-gluon plasma: There is no analytical method to describe deconfinement and hadronization in QCD. What one can do instead is to use lattice QCD, or apply approximation schemes that approach hadronization from high densities or high temperatures, where the theory is asymptotically free, and perturbative methods can be used. There are different techniques available to describe QCD at temperatures above deconfinement, with hard thermal loop re-summation as one example. This is a very active area of research in current nuclear theory. For the regime of heavy ion collisions, there still remains on problem: At temperatures above the deconfinement temperature T_c, say for T = 1 - 3 T_c, QCD is not yet completely free. Lattice calculations of energy density and pressure show a clear difference to the Stefan-Boltzmann limit, which corresponds to an ideal gas of quarks and gluons. So, this temperature regime is difficult to study with standard QCD techniques. Unfortunately, it is just this temperature regime that is reached in heavy ion collisions at RHIC, the relativistic heavy ion collider at Brookhaven.

(Do you have some fundamental problem with entering paragraphs? - But the context belongs together! - It looks completely unreadable. - Who reads that anyway? - I think I don't like your attitude.)


There was one big surprise in the experimental data from RHIC: it seems that the quark-gluon plasma created in the collisions has a very low viscosity, or is a most ideal liquid. At least, that is what can be concluded from the success of hydrodynamical simulations of RHIC collision simulating the quark-gluon plasma as an ideal liquid.

Here, one point is important to note: There is no way to measure the viscosity of the quark-gluon plasma directly. You have to infer it from the momentum distribution of final state hadrons, in this case, of the anisotropy of the momentum distribution of hadrons in the transverse plane for non-central collisions, which is called the elliptic flow.

(Insert explanation, link, graphics. - Good! Where is it? - I'm at home, can't access the journal. - Okay, lets do that tomorrow.)

Large values of elliptic flow are observed at RHIC, larger than what was expected from an extrapolation of the results from the CERN-SPS, where the collision energy is lower. As mentioned before, this RHIC elliptic flow can be reproduced using a hydrodynamical simulation of an ideal (zero viscosity) fluid for the deconfined phase. So, the conclusion is, the viscosity of the QGP is very low.

Here, there is one point to keep in mind: the actual viscosity is not known for sure, and model assumptions about the QGP go into it: Assumptions about the initial state used for the hydrodynamics simulation, for the equation of state and the properties of the hot and dense system, for hadronization, and for hadronic rescattering, i.e. the interactions of the hadrons in the still dense, but late phase of the collision. Moreover, the hydrodynamics code in use only now start to systematically investigate the effects of actual viscosity on the expansion dynamics.

The simulations using ideal hydrodynamics that are so successful in the reproduction of the elliptic flow use a so-called Glauber-dynamics initial state for the codes to run. But this initial condition is not the only game in town. For example, the so-called colour glass condensate (one model assumption for the high density, high-temperature initial state of the nuclear matter, where gluons are the main players) produces very high initial transverse momenta, which produce an elliptic flow consistent with data only if a viscosity is taken into account which is markedly higher than in the ideal fluid models used so far. So, a definite, uncontroversial answer about the the actual viscosity is still out. Obviously, lots of issues are not yet completely settled here.

When the first data on elliptic flow larger than expected before become known, Edward Shuryak pointed out that the very low viscosity which data seem to imply (but keep in mind that this fact as such is not completely waterproof yet) would be consistent with predictions of a very low viscosity of a supersymmetric Yang-Mills theory, and that this low viscosity corresponds to an absolute minimum of viscosity derived from the AdS/CFT duality and superstring theory. Hence, the term "most ideal liquid" was coined for the QGP created at RHIC, and it was argued that the strongly coupled QGP can be described using the analogy to the supersymmetric Yang-Mills theory.

Shuryak is a brilliant physicist, but it is also fair to say, we would say, that he is known in the community as someone who strongly promotes his ideas. And his ideas are often contested - as in this case, the idea of the "most ideal liquid" has been contested a lot, especially from the side of the promotors of the colour glass condensate. So, there is an ongoing debate in the community about these questions, the press releases about the ideal liquid notwithstanding. Anyway, this is our impression of how AdS/CFT entered the heavy ion community.

(It this the one who...? - Yes. - Do you really want to write that? I mean, I don't usally comment on people. - That is fair to say, believe me. And for the heavy ion people it's a compliment.)

Now, what does the AdS/CFT say, and where can it be applied? In brief - and corrections of experts on this are welcome - it helps to write down correlation functions in strongly coupled gauge theories from a duality to the dynamics of strings in an 10-dimensional AdS background with a boundary. Strings end on the boundary, which is Minkowski space, and end points of strings correspond to particles in the gauge theory. Problems of the mathematical exactness left beside, this is a unique and ingenious way to get information about correlation functions, which are very hard to obtain (or are not obtained yet) by lattice gauge theories or thermal field theory techniques.

Where has this duality been applied? The first case has been mentioned before: To calculate the viscosity of hot gauge theories, with the famous universal lower value of 1/4 pi. There are two more situations where it has been applied: To determine the screening of the interaction potential of a heavy quark-antiquark pair in a system moving in a background of hot gauge theory (An AdS/CFT Calculation of Screening in a Hot Wind by Hong Liu, Krishna Rajagopal, Urs Achim Wiedemann, hep-ph/0607062), and for jet quenching calculations, that is, to determine the energy loss of fast particles travelling through a hot medium. (Calculating the Jet Quenching Parameter from AdS/CFT, by the same authors: Hong Liu, Krishna Rajagopal, Urs Achim Wiedemann, hep-ph/0605178, now accepted as a PRL). As a sidenote, Wiedemann and Rajagopal are not string theorist, but have worked in heavy ion theory, QCD and nuclear theory. Hong Liu and Dam T. Son, one of the authors of the main viscosity reference, and also not a string theories by formation, will have plenary talks at Quark Matter, the main conference of RHIC physics.

Can these things be observed in heavy ion collisions? For the case of viscosity, we have discussed it before: there are some caveats, since viscosity can not be measured directly - you have to reproduce elliptic flow, and the inverse problem is not unique. The hot quark-gluon system may be a most ideal liquid, it may be something else, we do not know yet for sure. Screening of the potential is relevant for the so-called J/Psi suppression, but this is also something that has to be inferred backwards from the measured J/Psi yield, which is influenced by many other factors (the original idea iabout this is twenty years old now - however, there are still many open questions left).

At RHIC, there are chances from photons that may make these signals more waterproof than at CERN-SPS, but currently,. ambiguities remain. Jet quenching and energy loss is also a point where many calculations and models exist, but the inverse problem is very hard. So, we would say in all these three cases, you may have a very beautiful application of AdS/CFT to QCD at strong coupling, but the connection to experimental data is difficult and ambiguous.

You should not be disappointed: that is, unfortunately, very common in heavy ion physics. Take the original idea about J/Psi, or disordered chiral condensates, and many other examples: Signatures to check beautiful ideas are often washed out by lots of dirty QGP soup and hadron gas wind effects.

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2.Is it a hype?

Does the Global Positioning System (GPS) work because of General Relativity? One often hears this statement in discussions of General Relativity, and it is meant, we guess, to create an awareness that this arcane theory is true, and moreover has applications to down-to-earth technologies which are in every-day use. And as a matter of fact, it is true: The systematic effects on atomic clocks in orbit when observed from points on the surface of the earth as predicted by GR are incorporated into the system, and it all fits perfectly well!

On the other hand, to say that the GPS work because of General Relativity is an oversimplification which neglects the actual intricate details of the system, and which are, from a practical point of view, equally important for the workings of the GPS. A look in a technical description of the GPS will discuss lots off effects of the ionosphere and the atmosphere on the propagation of the satellite signals that have to be taken into account and corrected for - relativity often is not even mentioned! So, clearly, to say that the GPS work because of General Relativity is not wrong, but it is not the whole story: It is a catch phrase to show that GR is not some abstract mathematics, but plays indeed a role in the real world.

There is also a kind of inverse problem in the GPS example: Could one reconstruct GR from the GPS system alone? Could clever physicists derive GR from the systematic deviations in GPS, if they would not have been taken into account from the beginning? Well, they would only be partially successful, since, in fact, only some form of the equivalence principle is tested with the GPS, and not the full Einstein equations. To establish GR, more observations, such as the perihelion precession, are necessary.

To us, this seems to be very analogous to the situation of AdS/CFT in RHIC physics (To us? It was your comparison. I really like it but I like to point out it was your creativity at work here!) : There are applications of this fundamental duality to the physics of hot and strongly coupled QCD, and they probably contribute to the outcome of experiments. But there are many more, mundane effects coming into play, which influence final state hadronic data, and which make it very difficult to solve the inverse problem - to unambigously conclude an initial state.

For sure, AdS/CFT does not explain all of RHIC physics, so far, it seems, in our understanding, applicable to the regime of strongly coupled QGP above the deconfinement transition. What does it say about hadronisation, for example? Can it say something about this? That would be extremely cool, but it seems that there is no solution yet. Moreover, there seem to be open quastions in how far results derived for the supersymmetric Yang-Mills theory can, indeed, be carried over to QCD, see for example hep-ph/0608062.

These limitations of the AdS/CFT approach should also be mentioned, in our opinion, if only to avoid the misleading impression of string theorists showing up on the scene like the FBI agents with suits and sunglasses, take over the case from the dumb local police, and solve immediately what the locals have been unsuccessfully investigating for years.

(Couldn't find a nice pic of FBI agents, but I wasted some time on that. -- This is great!)

Besides this one should keep in mind that the AdS/CFT correspondence is an outcome of years of research of string theory. But it is not equal to string theory. Even if the current results show the usefulness of this correspondence, and make use of many developed techniques, what could this possibly tell us about string theory as a TOE? And then, the spacetime used there isn't really one that we would be interested in as a description of the world we live in - we come back to this in the last point.

These are some words of caution, but as Clifford pointed out:

"[...] applying string theory ideas - the whole shebang of strings, branes, black holes, gravity, etc - to understanding the new forms of matter being discovered at Brookhaven. This may welll be a great way of testing the remarkably intricate structures that string theory puts together and give us lots of clues about how to develop the theory better."

(You sure that's a good idea? - I don't want that to come out wrong either, I really like his point of view, esp. regarding the teapots and so on. And the fig jam. But I think it's okay, I mean we've made quite clear we aren't anti-string in any regard. - You really sure? - I have the comments forwarded on my BB, you think I want the beeps to keep me up all night?)

And this is understandibly something to get really excited about! Nevertheless, we can't avoid having the impression that string theorists must be pretty desperate if they try to justify their work with the calculation of a viscosity using a conjectured (unproven) side effect of the theory they have been working on. I am not aware of any work on how it would be possible to learn something about string theory as the TOE from observables in heavy ion collisions.

(Isn't that a bit hard, desperate? - Yes. I am not a nice girl in case you haven't mentioned. I want them to get the message. There's no need to be desperate. Nobody wants to kill string theory. But they should stay realistic.)

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3. What does it mean?

So, to us, it seems that AdS/CFT is a cool application and we would be happy to understand more about it. (? - !) On the other hand, there are caveats, and experimental verification of great ideas is difficult, as always, in heavy ion physics. But then, there is, we think, a more fundamental question about the ontological status of this duality: It is merely a computational tool, or should we really belief that the quarks and gluons we know and love are just the endpoints of strings in a 10-dimensional AdS×S⁵ space? (I am not really very much concerned with the ontology, honey. If it's the same, then it's the same, what's the point?)


This is probably a very general question, that can, and should, already be asked for the Ising model and the mother of all dualities, the Kramers-Wannier duality. In an experimental realisation of a two-dimensional Ising system, the elements of reality which are described by the Ising Hamiltonian are the magnetic moments of atoms. Or aren't they? Taking the duality serious, we could as well argue that no, not the magnetic moments are the real thing, but the dual plaquette variables. But does this make sense? Apparently not, especially since duality works for the Ising variables, the magnetic moments, but not for all other real things in the system, the atoms with all their electrons, and their nuclei.

Coming back to AdS/CFT, if it works for strongly coupled QCD, should we believe that the dual side, the strings, are real? Maybe, but then, the duality should work for all kinds of particles, not just strongly coupled quarks and gluons. Then, one could not discern any more between both sides of the duality mirror, and both sides could claim the same right to be the real thing. Or are we fundamentally wrong here? (Are we? What is reality anyhow? - I don't want to get into this right now. Can we just finish this &$%@ post?)

To summarize: Heavy Ion Physics does not equal strongly coupled QCD, and String Theory does not equal AdS/CFT. The calculations done using the AdS/CFT correspondence are wayleading and exciting. But the connections to string theory as a theory of everything, explaining quantum gravity, the parameters of the standard model, and more, are so far very weak and require more investigation.

Update: See also More on Ads/CFT and RHIC

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TAGS: SCIENCE, PHYSICS, STRING THEORY, NUCLEAR PHYSICS