AdS / CFT predicts the quark gluon plasma is unstable

The gauge-gravity duality is a spin-off from string theory and has attracted considerable attention for its potential to describe the quark gluon plasma produced in heavy ion collisions. The last news we heard about this was that the AdS/CFT prediction for the energy loss of quarks or gluons passing through the plasma does not agree with the data. The AdS/CFT community has so far been disappointingly silent on this issue, which has now been known for more than a year.

Meanwhile however, there has been an interesting new development pointed out by Brett McInnes in his papers

Fragile Black Holes and an Angular Momentum Cutoff in Peripheral Heavy Ion Collisions
Brett McInnes
arXiv:1201.6443

Shearing Black Holes and Scans of the Quark Matter Phase Diagram
Brett McInnes
arXiv:1211.6835

The dual description of the quark gluon plasma is a black hole in AdS space. Since the plasma resides in a beam pipe in a background metric that is to excellent approximation flat, the black hole that has to be used to describe it is a planar black hole. If one would use a “normal” spherical black hole, then the background for the plasma would have a spherical symmetry too.

These planar black holes appear alien at first sight because they have an infinitely extended planar horizon and are nothing like the real black holes that we have for example in the center of our galaxy. The planar black holes cannot in fact exist in an asymptotically flat space; they need the asymptotic AdS-space. So they might be alien in the context of astrophysics, but they make a lot of sense as a dual description for the quark gluon plasma.

Brett now notes the following. The quark gluon plasma that is created in heavy ion collisions generically has an angular momentum when the nuclei do not collide centrally. In particular, this angular momentum comes in the form of a shear, that is a non-trivial velocity potential in the direction parallel to the beam axis. The reason is, essentially, that the colliding heavy ions are approximately spherical (in their rest frame) and the amount of constituent particles that takes part in the collision depends on the distance from the beam axis. Thus arises a velocity profile.

So the quark gluon plasma has a shear. But this shear then should also be present in the dual description, ie for the black hole. In his paper, Brett studies such a sheared black hole in the AdS space – and the interesting thing is that he finds it to be unstable. If one takes into account that pairs of branes can be produced in the AdS background, then one can see that in fact an infinite amount of brane pairs can be produced because the brane action is unbounded from below.

But what does this mean?

The description of the quark gluon plasma that the AdS/CFT duality offers does not take into account that the formation, and subsequent fragmentation into hadrons, is a dynamical, time-dependent process. Brett thus argues that in a realistic situation after formation of the plasma it takes some while until the system is affected by the instability. He estimates the time it takes for the instability to develop and finds that for currently existing experiments at RHIC and at the LHC the plasma is stable for a time longer than it exists in the collision zone anyway. So there is nothing to observe in these experiments.

The relevant quantity here is the chemical potential. At RHIC and LHC it is very small, essentially because the collision is so highly energetic that very many particle-antiparticle pairs are created. However, for some upcoming new experiments, such as the ones planned at FAIR, that operate at a comparably low collision energy, the instability might become observable for realistic values of the impact parameter!

Brett is however very careful to point out that while the theoretic argument for the instability is solid, one should not take too seriously the numbers one obtains from his estimate. Since a truly dynamic treatment of the system is presently not feasible, what he does is instead is to calculate the time it takes for signals of an impending instability to propagate in the AdS background. One should not expect the result to be very precise.

Be that as it may, this opens the exciting possibility that upcoming experiments might observe an effect that could only be anticipated by use of the AdS/CFT duality.