For the last five years, physicists at the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory in the US have been producing the highest temperatures on Earth by colliding gold nuclei together at enormous energies. Their aim has been to recreate the extreme conditions that are thought to have existed during the first 10 microseconds of the universe, just before it cooled enough for the quarks and gluons created in the Big Bang to combine and form the protons and neutrons that make up the world around us.

The possibility of creating such a “quark-gluon plasma” has tantalized researchers since circumstantial evidence for such a state was seen at CERN in 2000. But those results were inconclusive because the plasma existed only fleetingly. It was assumed that the higher energies available at RHIC would allow the quark-gluon plasma to be studied in detail, and two years ago physicists at the collider said that they had come closer than ever before to creating the exotic new state of matter (see “The RHIC gold rush” Physics World June 2003 pp31-35).

Now, RHIC’s four experimental collaborations – STAR, PHENIX, PHOBOS and BRAHMS – have found the most convincing evidence to date that a quark-gluon plasma has been created. But instead of behaving like a gas of free quarks, antiquarks and gluons as expected, the hot droplet of matter behaves more like a liquid. In fact, the RHIC results suggest that it could be the most perfect liquid ever created (www.bnl.gov/bnlweb/pubaf/pr/docs/Hunting-the-QGP.pdf; Nucl. Phys. A at press ).

But the really intriguing aspect of the result – presented at the April meeting of the American Physical Society in Tampa, Florida – is that string theory has been mentioned for the first time in the announcement of a major experiment.

Perfect liquid

The quark-gluon plasma is predicted to exist by quantum chromodynamics (QCD), the theory of the strong interaction. In QCD, protons and neutrons are treated as bound states of quarks, which are held together by the exchange of gluons. At distances much shorter than the size of a proton or neutron (about 10^-15 m), the quarks and gluons behave as free particles. However, as the distance between two quarks increases the force between them becomes very strong.

At low energies or temperatures quarks and gluons prefer to bind together in clusters that contain three quarks (such as the proton and neutron), or a quark and an antiquark (such as a pion or kaon). However, at energies corresponding to temperatures above about 10¹³ K the average distance between these particles becomes so small that matter behaves like an ideal gas of free quarks and gluons.

Even before RHIC was turned on, most of us anticipated that it would be difficult to pinpoint a decisive signal for the formation of a quark-gluon plasma. Although the collision energy at RHIC (200 GeV per nucleon) is about 10 times higher than it was at CERN, most of this energy ends up in the various remnants of the gold nuclei, leaving only a small fraction to do the useful job of creating the new state. Furthermore, because the plasma takes time to expand, most of the particles that are actually detected come from the later stages of the collision, when the plasma has cooled substantially. However, by measuring the total number of particles produced, and also their energies, it is possible to indirectly study the state initially created by the gold collisions.

As many measurements at RHIC indicate, this system is not a simple, weakly interacting gas of quarks and gluons. Instead, the super-hot state appears to be strongly coupled, which complicates things considerably. Since very few reliable calculations can be made in the strong-coupling regime, researchers cannot be absolutely sure that a quark-gluon plasma has been created.

What does seem certain, however, is that the new RHIC state behaves as if it were a droplet of a perfect liquid – i.e. a fluid with almost zero viscosity. A weakly coupled quark-gluon system, on the other hand, would have a high viscosity. This conclusion was reached by studying events in which the gold nuclei undergo glancing rather than head-on collisions, which result in an initial hot region that is almond shaped rather than round. A perfect liquid that initially fills such a region will expand mostly along the shorter dimension of the almond, since the pressure changes fastest in this direction. A gas of free particles, in contrast, would expand uniformly in all directions.

In the perfect-liquid scenario the typical momentum of the outgoing particles therefore depends strongly on their direction, while it is independent of direction in the gas scenario. In between these two states is a non-perfect fluid (i.e. with a non-zero viscosity, such as water). Using hydrodynamic models, theorists have been able to reproduce the asymmetry of the observed spectrum, which is technically called the elliptic flow, assuming the fluid has zero or very small viscosity.

String connection

So, what does all this have to do with string theory? Unlike QCD and other quantum field theories, string theory treats all particles as tiny vibrating strings. It also provides an appealing framework for unifying all four forces in nature, including gravity, although one possible drawback of string theory is that it requires six or more extra spatial dimensions in addition to the three that we know.

In 1997 Juan Maldacena, then at Harvard University, revolutionized our understanding of strongly coupled quantum field theory by proposing a concrete example of two seemingly unrelated theories that could, in fact, describe the same system. One of these theories lives in the familiar four dimensions of space-time and is similar to QCD; the other theory is a type of string theory that lives in a curved 10D space. The relationship between the two theories stems from the fact that the QCD-like theory lives on a “membrane” that is immersed in the higher-dimensional space.

Remarkably, when the particles in the 4D theory interact strongly with one another, such as the interactions between quarks at long distances, the equivalent string theory becomes simple and can be solved exactly. Maldacena’s conjecture thus allows us to calculate observables in the strong-coupling regime where no previous method works. The caveat of the new approach is that it can only be applied for a small class of theories that are strongly coupled at all distances. And this class unfortunately does not include QCD, which is weakly coupled at short distances.

In this narrow class of theories, the hot plasma in the 4D theory corresponds to a black hole in the 10D equivalent description, which matches very well with Stephen Hawking’s prediction that black holes have temperature. Moreover, there is a direct relationship between vibrations in the plasma, such as sound waves, and vibrations of the black-hole horizon. For example, when an object is dropped into the black hole in 10D, the equivalent picture in 4D is a hot, expanding region that dissolves into a plasma. Using this equivalence, various theorists, including the present author, have deduced that if such plasmas were real, they would be almost perfect liquids.

Since Maldacena’s conjecture does not apply to QCD, however, the viscosity of the real quark-gluon plasma cannot be computed via string theory. This makes the RHIC announcement that the viscosity of its plasma is comparable to the values one finds from string-theory calculations even more surprising. If this is true, the quark-gluon plasma created at RHIC could be the most perfect fluid in nature. This in itself is an interesting fact, but it could also indicate that string theory has some relation to real QCD. However, we first need more quantitative evidence from RHIC, such as an upper bound on the viscosity.

Coincidentally, researchers are currently homing in on the strong-coupling regime in a completely different field of physics: ultracold atomic gases. The strong coupling between the atoms in these systems can be achieved by fine-tuning an external magnetic field. By watching the oscillations of the gases in the trap, researchers have found that the oscillations live longer when the coupling is larger, indicating that the viscosity of such gases is small in the strong-coupling regime. In the search for the most perfect fluid, it seems that heavy-ion physicists will face strong competition.