AdS/CFT confronts data

One of the most persistent and contagious side-effects of string theory has been the conjectured AdS/CFT correspondence (that we previously discussed here, here and here). The briefest of all brief summaries is that it is a duality that allows to swap the strong coupling limit of a conformal field theory (CFT) with (super)gravity in a higher dimensional Anti-de-Sitter (AdS) space. Since computation at strong coupling is difficult, at the very least this is a useful computational tool. It has been applied to some condensed matter systems and also to heavy ion physics, where one wants to know the properties of the quark gluon plama. Now the theory that one has to deal with in heavy ion collisions is QCD, which is neither supersymmetric nor conformal, but there have been some arguments for why it should be approximately okay.

The great thing about the application of AdS/CFT to heavy ion physics is that it made predictions for the LHC's heavy ion runs that are now being tested. One piece of data that is presently coming in is the distribution of jets in heavy ion collisions, but first some terminology.

A heavy ion is an atom with a high atomic number stripped of all electrons; typically one uses lead or gold. Compared to a proton, a heavy ion is a large clump of bound nucleons (neutrons and protons) that are accelerated and brought to collision. They may collide head-on or only peripherally, quantified in a number called "centrality." When the ions collide, they temporarily form a hot, dense soup of quarks and gluons called the "quark gluon plasma." This plasma rapidly expands and cools and the quarks and gluons form hadrons again (in a process called "hadronization" or also "fragmentation"), that are then detected. The temperature of the plasma depends on the energy of the colliding ions that is provided by the accelerator. At RHIC the temperature is about 350 MeV, in the LHC's heavy ion program it is about 500 MeV. The task of heavy ion physicists is to extract information about matter at nuclear densities and such high temperatures from the detected collision products.

A (di) jet is two back-to-back correlated showers of particles that are a typical signature in perturbative QCD. It is created if a pair of outgoing partons (quarks or gluons) hadronizes and produces a bunch of particles that then hit the detector. Since QCD is confined, the primary, colored, particles never reach the detector. In contrast to proton-proton collisions, in heavy ion collisions the partons have to first go through the quark gluon plasma before they can make a jet. Thus, the distribution of momenta of the observed jets depends on the properties of the plasma, in particular the energy loss that the partons undergo.

Different models predict different energy loss and dependence of that energy loss on the temperature of the medium. Jets are a QCD feature at weak coupling and strictly speaking in the strong coupling limit that AdS/CFT describes there are no jets at all. What one can however do is to use a hybrid model in which one just extracts the energy loss in the plasma from the conformal theory. This energy loss scales with L³ T⁴, where L is the length that the partons travel through the medium and T is the temperature. All other models for the energy loss scale with smaller powers of the temperature.

Heavy ion physicists like to encode observables into how different they are from the corresponding observables for collisions of the ion's constituents. The "nuclear suppression factor," denoted R_AA, plotted in Thorsten Renk's figure below (Slide 17 of this talk), is basically the ratio of the cross-section for jets in lead-lead over the same quantity for proton-proton (normalized to the number of nucleons) and it's depicted as a function of the average transverse momentum (p_T) of the jets. The black dots are the ALICE data, the solid lines are fits from various models. The orange line at the bottom is AdS/CFT.


[Picture credit: Thorsten Renk, Slide 17 of this presentention]
As the saying goes, a picture speaks a thousand words, but since links and image sources have a tendency to deteriorate over time, let me spell it out for you: The AdS/CFT scaling does not agree with the data at all.

A readjustment of parameters might move the total curve up or down, but the slope would still be off. Another problem with the AdS/CFT model is that the model parameters needed to fit the RHIC data are very different from the ones needed for the LHC. The model that does best is Yet another Jet Energy-loss Model (YaJEM) that works with in medium showers (I know nothing about that code). It is described in some detail in this paper. It doesn't only fit well with the observed scaling, it also does not require a large readjustment of parameters from RHIC to LHC.

Of course there's always caveats to a conclusion. One might criticize for example the way that AdS/CFT has been implemented into the code. But the scaling with temperature is such a general property that I don't think nagging at the details will be of much use here. Then one may want to point out that the duality is good actually only in the large N limit and N=3 isn't so large after all. And that is right, so maybe one would have to take correction terms more seriously. But that would then require calculating string contributions and one loses the computational advantage that AdS/CFT seemed to bring.

Some more details on the above figure are in Thorsten Renk's proceedings from the Quark Matter 2011, on the arxiv under 1106.2392 [hep-ph].

Summary: I predict applications of the AdS/CFT duality to heavy ion physics is a rapidly cooling area.