AdS/CFT and Heavy Ion Collisions at RHIC and LHC Hong Liu Massachusetts Institute of Technology

QCD QCD has presented us many fascinating dynamical phenomena: Confinement, chiral symmetry breaking, asymptotic freedom, internal structure of nucleons …… largely guided by experiments, great challenges for theorists. Recently, heavy ion collision experiments opened new windows into probing dynamical phenomena in QCD: The above phenomena concerns vacuum structure of the theory Even in QED, which is much simpler than QCD, once going to many-body system, completely New dynamical phenomena can appear, Quantum hall effect, superconductivity……. Many body physics, collective phenomena, ……. thermalization, finite temperature, ……

Small baryon density : Smooth crossover at

Relativistic heavy ion collisions RHIC (2000): Au+Au : center of mass energy per pair of nucleons Au: 197 nucleons; Total: 39.4 TeV Temperature (1 fm after collision) ~ 250 MeV Baryon chemical potential ~ 27 MeV Deconfinement crossover in QCD: TC ~ 170 MeV LHC: Pb + Pb (2009)

QCD Phase diagram LHC RHIC One very interesting feature is that with a small baryon number density. one finds a smooth crossover in the transition from the hadronic phase to the QGP, like ionization of a gas. At larger baryon density, the transition becomes First order. In this region there is some more exciting physics which I will not have time to discuss today. Maybe Krishna can tell you some other time.

Quark-gluon liquid Experiments at RHIC suggest: At T ~ 1.5 TC , the quark-gluon plasma (QGP) is so strongly coupled that it is better thought of as a liquid than a gas. A B Evolution well described by ideal hydrodynamics (very small viscosity)

according to perturbative QCD calculations Water

How to calculate properties of a strongly coupled QGP liquid? Lattice calculations: great for static (thermodynamic) properties dynamical quantities: scarce and indirect Perturbative QCD calculations: right theory, wrong approximation

String theory to the rescue!

AdS/CFT correspondence Maldacena (1997), Gubser, Klebanov,Polyakov; Witten (1998) Classical gravity in a higher dimensional spacetime Strongly coupled gauge theories Finite temperature QGP Black hole Infinite families of examples are known, including gauge theories which are: conformal or nonconformal confining or non-confining supersymmetric or non-supersymmetric

AdS: anti-de Sitter spacetime (negative cosmological constant) (3+1)-dim world, Finite Temperature AdS event horizon (black hole) AdS: anti-de Sitter spacetime (negative cosmological constant) Our (3+1)-dimensional world lies at the boundary of AdS.

However, it is NOT yet known what is the gravity description of QCD.

Strategy Understand QGP properties in other theories which are analyzable at strong coupling and compare with experiments. (wrong theory, right approximation) new discovery machine, look for universality “Ising model’’ for QCD QGP: N=4 Supersymmetric Yang-Mills at finite T two parameters: NC , scale invariant Large NC , large λ limit: “easy’’ to calculate

Purpose of the talk Describe some of the dynamical insights into properties of strongly coupled plasma obtained from AdS/CFT: Thermodynamic properties Shear viscosity Jet quenching heavy quark diffusion Quarkonium suppression (a prediction from string theory)

Q1: Thermodynamics N=4 SYM: Gubser, Klebanov, Peet Thermodynamics of very weakly and very strongly coupled plasmas can be similar. Infinite families of gauge theories (with different gauge groups and matter contents) share similar properties: Nishioka, Takayanagi

Weak dependence on T of in the range TC ~ 4 TC RHIC Karsch hep-lat/0106019 QCD: Weak dependence on T of in the range TC ~ 4 TC approximately scale invariant

Q2: Shear viscosity For all known strongly coupled QGPs with a gravity description: Policastro, Son, and Starinets Kovtun, Son and Starinets Buchel, J. Liu Conformal or not, supersymmetric or not, chemical potential or not, confining at T=0 or not, having fundamentals or not with varying number of degrees of freedom QCD: The only other system which comes close: strongly coupled cold atomic gas

Universality ? We now know infinite classes of different QGPs: similar thermodynamical properties universality of shear viscosity Is QCD at T~ a few TC in this class? To what observables does the universality apply ?

Q3:Jet Quenching High energy partons lose energy quickly in the QGP 10-20 GeV jet High energy partons lose energy quickly in the QGP ???? an excess of low energy particles redistributed to rather large angles The dominant effect of the medium on a high energy parton is medium-induced Bremsstrahlung. : reflects the ability of the medium to “quench” jets. encodes all the soft physics (in the high energy limit )

Jet Quenching parameter Experimental estimate: : 5-15 GeV2/fm Perturbation theory: : < 1 GeV2/fm From N=4 SYM: HL, Rajagopal, Wiedemann is NOT proportional to the number of scattering centers.

Universality of ? A family of conformal field theories (CFT) with a gravity dual: (large N and strong coupling) HL,Rajagopal Wiedemann, sCFT : entropy density Estimate for QCD:

Q4: Heavy quarks moving in a QGP Considering a very heavy quark moving in a QGP, is it more like an electron moving in the water (point-like, bremsstrahlung) or a bullet moving in the water (described by hydrodynamics) not known in QCD

A moving quark in a strongly coupled N=4 plasma See also Gubser, Pufu and Yarom Chesler , Yaffe, 0712.0050

A prediction from string theory

Heavy quarkonia as probes of QGP A hallmark of QGP is that it screens color objects. The potential between the quark and anti-quark in a quarkonium bound state is sensitive to the screening of the plasma. They dissociate at Td > TC Heavy ion collisions: color screening in the produced medium J/ψ suppression Matsui and Satz (1987)

Screening of heavy quarks in QCD Heavy quark potential for T > TC O.Kaczmarek, F. Karsch, P.Petreczky, F. Zantow, hep-lat/0309121 Screening length: Heavy ion collisions: Q and Qbar move relative to the plasma screening at finite velocity ? (not known)

Screening in N=4 SYM V(L): potential between a Q and Qbar LS(T) L Similar to QCD above TC

Finite velocity scaling HL,Rajagopal,Wiedemann Chernicoff, Garcia, Guijosa Moving at a finite velocity v Peeters, Sonnenschein, Zamaklar Finding string shape of minimal energy Event horizon Dissociation temperature:

I will now assume a similar scaling applies to QCD Dissociation temperature:

A prediction from string theory HL,Rajagopal,Wiedemann zero velocity : (lattice) : Tdiss ~ 2.1 TC Asakawa, Hatsuda; Datta, Karsch, Petreczky, Wetzorke : Tdiss ~ 3.6 TC RHIC ~1.5 Tc LHC? Could lead to significant suppression at large PT. J/ψ RHIC This effect may be tested at RHIC II or LHC

Nuclear modification factor RAA Double the pT range to 10GeV/c Consistent with no suppression at high pT: RAA(pT>5 GeV/c) = 0.89±0.20 Indicates RAA increase from low pT to high pT Different from expectation of most models: AdS/CFT: H. Liu, K. Rajagopal and U.A. Wiedemann, PRL 98, 182301(2007) and hep-ph/0607062 Two Component Approach: X. Zhao and R. Rapp, hep-ph/07122407 Quark Matter 2008, Jaipur, India, Feb. 4-10, 2008 Zebo Tang, USTC/BNL

Propagation of mesons in QGP Does the screening affect the propagation of mesons in a QGP? Mateos, Myers and Thomson Speed limit : Ejaz, Faulkner, HL, Rajagopal, Wiedemann As , This could also lead to observable effects.

Heavy ion collisions and AdS/CFT String theory techniques provide qualitative, and semi-quantitative insights and predictions regarding properties of strongly interacting quark-gluon plasma. Many other things I did not have time to discuss “Wrong theory, right approximation” appears to work much better than “right theory, wrong approximation” Universality? Thank You