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

2. 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, ……

3. Small baryon density :
Smooth crossover at

4. 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)

6. 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.

7. 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)

8. according to perturbative
QCD calculations
Water

9. 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

10. String theory to the rescue!

11. 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

12. 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.

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

14. 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

15. 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)

16. 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

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

18. 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

19. 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 ?

20. 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 )

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

22. 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:

23. 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

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

25. A prediction from string theory

26. 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)

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

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

29. 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:

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

31. 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

33. 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, (2007) and hep-ph/
Two Component Approach:
X. Zhao and R. Rapp, hep-ph/
Quark Matter 2008, Jaipur, India, Feb. 4-10, 2008
Zebo Tang, USTC/BNL

34. 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.

35. 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