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Edward Shuryak is a Professor of Physics and the Director of Center for Nuclear Theory at Stony Brook University.

QGP - New Frontiers

By Edward Shuryak

This is a summary of my final talk at Quark Matter 2008 [1] containing brief review of recent theory developments and discussion of where we should go from here. Particular fundamental questions to be addressed: Why is sQGP such a good liquid? Do we understand deconfinement? Can we apply AdS/CFT correspondence to understand rapid equilibration and entropy production at RHIC?

A paradigm shift in our field, which occurred during 2003-2004 and resulted in "discovery" workshop and experimental "white papers," have affected theory developments in a profound way. Since that time we all had to learned a lot of new physics. Some of it came from other fields, including physics of strongly coupled plasmas and trapped ultracold gases with large scattering length. String theory gave us a remarkable tool, known as AdS/CFT correspondence, which forced us to learn also physics of black holes. Clearly it was impossible to discuss all that in a QM08 talk, and even less possible here: thus I just touch on few main points.

1   New hydrodynamics, now at the O(10%) level

Hydrodynamical description of the QGP phase supplemented by hadronic cascades [2] provides excellent description of RHIC data. Radial and elliptic flow of various secondaries as a function of centrality and rapidity are reproduced till p_t ∼ 2 GeV, or for 99% of particles. CuCu data match AuAu well, suggesting that even Cu is large enough to be treated hydrodynamically. On top of that there is a conformation of "conical flow" [3] from 3-particle correlations by STAR and PHENIX. This lead to now famous statement that QGP is the most perfect liquid known.

Now, how perfect is QGP? A new round of studies focused on this issue use the so called second order formalism, which includes viscosity and relaxation time. The first results by P. and U.Romatschke [4] found that the best fits one can reach with η/s ∼ .03, which is even smaller than the famous AdS/CFT result [5] η/s=1/4π. Small viscosity effects were also found by Teaney and Dusling [6] and by Chaudhuri [7] who gave a plenary talk. D.Molnar[8] have demonstrated also nice agreement between cascades and hydro for v₂(p_t), with appropriately tuned cross sections/viscosity. (Song and Heinz [9] however found for some reason larger corrections.)

Have we really reached an accuracy level which allows to get reliable value of η/s? The uncertainties in initial state deformation [11] are not large, at the 10% level, but comparable to the viscosity effect. EoS from the lattice can probably be constrained better, as are uncertainties in hadronic state/freezeout. Thus η/s ∼ 0.1 is definitely still possible: but not much larger than that.

Can it be even smaller? Yes: even in AdS/CFT context, Lublinsky and myself [10] found that effective viscosity η(k) is decreasing with momentum k from its value at k=0. We don't understand why is it; but if so it is important at very early stages (thin almond).

2   A magnetic side of QGP

Long ago G.'t Hooft and Mandelstam [12] have proposed a model of confinement due to a "dual superconductor," with Bose-condensed magnetically charged objects expelling (gluon) electric field into the flux tubes. Seiberg and Witten [13] have shown how it works in the N=2 super Yang Mills theory. J. Liao and myself [14] realized that QGP right above T_c should have a lot of magnetic monopoles, from melted "dual superconductor," which is confirmed by recent lattice data (see refs in [1]).

One point I would like to make is electric-magnetic competition. An electric charge entering a region of space with the magnetic field often makes Larmor semicircle and gets reflected. Thus the Lorentz force produce a pressure on a magnetic field, trying to expel magnetic field into flux tubes. We know how this works in superconductors or in (e.g. solar) plasmas. Dual to that is a picture of monopole plasma expelling electric field into flux tubes, not only in confined (superconductor) phase, but in a QGP phase as well [15]. The second important general point is that electric and magnetic coupling constants are related by the celebrated Dirac quantization condition
 

αs(electric)αs(magnetic)=1

(1)

which demands that they must run in the opposite directions: when α_s(electric)=e²/4π is small (high T), α_s(magnetic)=g²/4π is strong and vice versa. How this looks in the schematic phase diagram is shown in Fig.1.

Figure 1: (color online) A schematic phase diagram on a ("compactified") plane of temperature and baryonic chemical potential T−μ. The (blue) shaded region shows "magnetically dominated" region g < e, which includes the e-confined hadronic phase as well as "postconfined" part of the QGP domain. Light region includes "electrically dominated" part of QGP and also color superconductivity (CS) region, which has e-charged diquark condensates and therefore obviously m-confined. The dashed line called "e=g  line" is the line of electric-magnetic equilibrium. The solid lines indicate true phase transitions, while the dash-dotted line is a deconfinement cross-over line

Lattice data show that electric-magnetic equilibrium, when α_s(electric)=α_s(magnetic)=1 happens to be at T ≈ 1.5T_c, right in the RHIC domain. One may think that viscosity has a minimum here, as both electrically charged quasiparticles (quarks) and magnetically charged (monopoles) have difficulty propagating. This is confirmed by molecular dynamics simulations we made for novel types of plasmas, including electric and magnetic charges [14]: the minimum is when a mixture is 50-50%.

The reason why the collision rate is enhanced and diffusion/viscosity reduced in such plasmas can be explained very simply. Imagine one of the particles - e.g. a quark. The Lorentz force makes it rotate around a magnetic field line, which will bring it toward one of the nearest monopoles. Bouncing from it it will go to an antimonopole, and then bounce back again: like electrons/ions do in the so called magnetic bottle. (By the way, invented in 1950's by one of my teachers G.Budker.) Thus particles are all well trapped by each other, and the ensemble can only expand/flow collectively.

3   AdS/CFT duality description for sQGP

Relation between RHIC physics and string theory was discussed in RHIC News by P.Kovtun[16]. He mention several applications, including thermodynamics, transport coefficients and even conical flow, as a holographic image of a string trailing a moving charge (jet). All of them correspond to near-equilibrium physics.

I considered in QM08 talk a new frontier to be AdS/CFT usage out of equilibrium, to address the most difficult question of RHIC physics: how does initial equilibration (entropy production) happen. The so called "glasma" is a non-equilibrium state preceding QGP. So far it was modeled by random gluon field created in heavy ion collisions via classical Yang-Mills equation in weak coupling (see e.g. L.McLerran [17]). however, as the corresponding scale Q_s at RHIC is only about 1 GeV, not far from parton momenta in QGP behaving in a strongly coupled regime, one may instead use strong coupling tools.

I called this approach sGLASMA; it was recently attempted by S.Lin and myself [18] using AdS/CFT. In this setting the problem reduces to a question how cold T=0 "extremal" black hole (AdS) becomes hot (non-extremal) one, with a horizon, nonzero temperature and entropy. The setting includes charges moving by straight lines after the collision, as usual, which are the endpoints of strings. Unlike familiar Lund model (Pythia), those strings are not breaking but falling into the 5-th direction toward the black hole, see fig.2.

Figure 2: Schematic view of the collision setting. The classical heavy charges move along directions x_± and collide at the origin. String snapping leads to longitudinally stretched strings (wide black line) which are also extended into the 5-th dimension toward the AdS center.

For one string one can both solve equations of falling and even find its (gravitational) hologram (image in our world): the result is an explosion shown in fig.3. This is a AdS/CFT analog of a jet: it is non-hydrodynamical, as one can see from stress tensor itself.

Figure 3: The contours of momentum density T⁰ⁱ in transverse plane. The magnitude is represented by color, with darker color corresponding to greater magnitude. The direction of the momentum flow is indicated by arrows

For many strings falling together their combined gravity is non-negligible, so one should solve non-linearized Einstein equations. Then a horizon is created leading to a loss of information (=entropy production) and a hydrodynamical explosion. This last part is what we and others are working on right now.

People thinking about possible outcomes of LHC experiments dream about possibility of black hole production. What I am saying is that RHIC heavy ion collisions do produce a black hole, in each and every event - but in the AdS/CFT sense, in the effective gravity in the 5-th dimension. (This dimension is not real: it is just a mathematical trick to solve the problem, something like an imaginary axes of complex analysis.)

References

[1] See slides e.g. at http://dau2.physics.sunysb.edu/ shuryak/talks.html

[2] D. Teaney, J. Lauret and E. V. Shuryak, arXiv:nucl-th/0110037. T. Hirano, Acta Phys. Polon. B 36, 187 (2005) [arXiv:nucl-th/0410017]. C. Nonaka and S. A. Bass, Phys. Rev. C 75, 014902 (2007) [arXiv:nucl-th/0607018].

[3] H. Stoecker, "Collective Flow signals the Quark Gluon Plasma," Nucl. Phys. A 750, 121 (2005) [arXiv:nucl-th/0406018]. J. Casalderrey-Solana, E. V. Shuryak and D. Teaney, hep-ph/0411315. hep-ph/0602183.

[4] P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99, 172301 (2007) [arXiv:0706.1522 [nucl-th]].

[5] G. Policastro, D. T. Son and A. O. Starinets, Phys. Rev. Lett. 87, 081601 (2001) [arXiv:hep-th/0104066].

[6] K. Dusling and D. Teaney, arXiv:0710.5932 [nucl-th].

[7] A. K. Chaudhuri, arXiv:0801.3180 [nucl-th].

[8] D. Molnar, arXiv:0707.1251 [nucl-th].

[9] H. Song and U. W. Heinz, arXiv:0712.3715 [nucl-th].

[10] M. Lublinsky and E. Shuryak, Phys. Rev. C 76, 021901 (2007) [arXiv:0704.1647 [hep-ph]] and work in progress.

[11] T. Lappi and R. Venugopalan, Phys. Rev. C 74, 054905 (2006) [arXiv:nucl-th/0609021].

[12] S. Mandelstam, Phys. Rept. 23, 245 (1976).
G. 't Hooft, Nucl. Phys. B 190, 455 (1981).

[13] N. Seiberg and E. Witten, Nucl. Phys. B 426, 19 (1994) [Erratum-ibid. B 430, 485 (1994)] [arXiv:hep-th/9407087].

[14] J. Liao and E. Shuryak, "Strongly coupled plasma with electric and magnetic charges," Phys. Rev. C 75, 054907 (2007) [arXiv:hep-ph/0611131].

[15] J. Liao and E. Shuryak, arXiv:0706.4465 [hep-ph].

[16] P.Kovtun, RHIC News, Sept.11,2007

[17] L.McLerran, RHIC News Jan.30,2008

[18] S. Lin and E. Shuryak, arXiv:0711.0736 [hep-th]. arXiv:hep-ph/0610168.

The Relativistic Heavy Ion Collider at Brookhaven National Laboratory is a world-class scientific research facility primarily funded by the U.S. Department of Energy Office of Science. Hundreds of physicists from around the world use RHIC to study what the universe may have looked like in the first few moments after its creation. What physicists learn from these collisions may help us understand more about why the physical world works the way it does, from the smallest subatomic particles, to the largest stars.