Transcript String theory, black holes and relativistic heavy ion
String theory and heavy ion collisions
Hong Liu Massachusetts Institute of Technology HL, Krishna Rajagopal, Urs A. Wiedemann hep-ph/0605178, PRL in press hep-ph/0607062, submitted to PRL and to appear
String theory and heavy ion collisions
Son and Kapusta’s talks
The AdS/CFT computation of the shear viscosity: • could ``explain’’ the perfect fluid observed at RHIC • possibly a universal lower bound Here, I would like to convince you this is likely to be the first chapter of a long story .
In later chapters, many more experimental results be explained, and predictions can be made. could
Chapter n: AdS/CFT and Jet quenching
Parton energy loss in QGP
The dominant effect of the medium on a high energy parton is medium-induced Bremsstrahlung.
E
2
S N C q
ˆ
L
2 Baier, Dokshitzer, Mueller, Peigne, Schiff (1996):
q
ˆ : reflects the ability of the medium to “quench” jets.
q
ˆ
k T
2
L
2 : Debye mass : mean free path
Wanted
: a first principle computation of
q
ˆ
q
ˆ : 5-15 GeV 2 /fm
New theoretical techniques needed !
• The main theoretical techniques for dealing with strongly coupled problems are lattice calculations . • Lattice techniques are not well adapted to calculate transport coefficients , or dynamical processes of any sort.
AdS/CFT correspondence
Maldacena (1997), Gubser, Klebanov,Polyakov; Witten (1998)
N
= 4 Super-Yang-Mills theory in 4d with SU(N C ) A string theory in 5d AdS Finite temperature Large N C and strong coupling limit Black hole in AdS 5 Classical gravity limit YM observables at infinite N C and infinite coupling computed using classical gravity can be Apply to both dynamical and thermodynamic observables .
Strategy
• Need a non-perturbative definition of
q
ˆ
q
ˆ Mills theory using AdS/CFT Similar strategy was used to compute the shear viscosity.
N
Caution: = 4 Super-Yang-Mills theory is NOT QCD Using sQGP of
N
Later: = 4 SYM to understand sQGP of RHIC may NOT be far-fetched.
Now: Accumulate data points
q
ˆ
: a non-perturbative formulation
Hard: weakly coupled Soft: likely strongly coupled
q
ˆ : multiple rescatterings of hard particles with the medium
Soft scatterings
Zakharov (1997); Wiedemann (2000) • Amplitude for a particle propagating in the medium • High energy limit (eikonal approximation): Soft scatterings are captured by Light like Wilson lines.
A non-perturbative definition of
q
ˆ Wiedemann (2000) Light-like Wilson loop:
L
L : conjugate to the p T
L
:
length of the medium Assuming:
L
1 /
T
L
Thermal average (Hard to calculate using lattice) Nonperturbative definition of
q
ˆ
Wilson loop from AdS/CFT
Maldacena (1998); Rey and Yee (1998) Recipe: Our (3+1)-dim world, Wilson loop C in our world
r
S
(
C
) : area of string worldsheet with boundary C horizon Black hole in AdS spacetime: • radial coordinate r, • horizon: r=r 0
r
0
Finding S(C)
• Wilson loop can be considered as the spacetime trajectories of a quark and antiquark pair.
• Key: open string connecting the quark pair can venture into the radial dimension.
• Finding S (C) : finding the shape of the string hanging from the spatial infinity of a black hole. Not more difficult than finding the Catenary !
Shape of the string
=
r=r 0 The string hangs down from infinity and touches the horizon.
Interactions between the quark and the medium Interaction of the string with the horizon of a black hole.
q
ˆ
of
N
=4 SYM theory
BDMPS transport coefficient reads:
q
ˆ
SYM
3 / 2 4 4
T
3 26 .
69
SYM N c T
3 • It is not proportional to number of scattering centers • Take:
N C
3 ,
s
1 2 ,
T
300
MeV SYM
4.5
GeV 2 /fm.
• Experimental estimates: 5-15 GeV 2 /fm
Jet quenching in a wind
We have assumed that the medium is static , in realistic situations the medium itself can be moving:
q
ˆ 1 1
V
2 1
V
Cos
q
ˆ 0 : the angle between the velocities of the quark and the medium
V
Example: : velocity of the medium 2 ,
V
0 .
5 ,
q
ˆ 1 .
15
q
ˆ 0
q
ˆ
SYM
5 .
2
GeV
2 /
fm
HL,Rajagopal Wiedemann
Summary
• In QGP of QCD, the energy loss of a high energy parton can be described perturbatively up to a non-perturbative jet-quenching parameter .
• We calculate the parameter in
N
=4 SYM ( not necessarily full energy loss of SYM) • It appears to be close to the experimental value.
Is the agreement meaningful?
Is agreement meaningful?
N
=4 SYM theory • Conformal • no asymptotic freedom, no confinement • supersymmetric • no chiral condensate • no dynamical quarks, 6 scalar and 4 Weyl fermionic fields in the adjoint representation.
Physics near vacuum and at very high energy is very different from that of QCD
Is agreement meaningful? (continued)
N
=4 SYM at finite T • conformal QCD at T ~T C -3 T C • near conformal ( lattice ) • no asymptotic freedom, no confinement • not intrinsic properties of sQGP • supersymmetric ( badly broken ) • not present • no chiral condensate • not present • no dynamical quarks, 6 scalars and 4 fermions in the adjoint representation.
• may be taken care of by proper normalization
Maybe the agreement is not an accident after all !
Take:
q
ˆ
SYM
3 / 2 4 4
T
3 26 .
69
SYM N c T
3
N C
3 ,
s
1 2 ,
T
300
MeV SYM
4.5
GeV 2 /fm.
Experimental estimates: 5-15 GeV 2 /fm Caveat: AdS/CFT calculation is in the infinite N C and infinite coupling limit
q
ˆ
for other theories
• General conformal field theories (CFT) with a gravity dual: (large N and strong coupling)
q
ˆ
CFT N
4
a CFT a N
4 a CFT : central charge • Theories near conformal: corrections small Buchel • Finite coupling and N C corrections: hard • R-charge chemical potentials: Armesto, Edelstein and Mas corrections mall when chemical potential is small Lin , Matsuo , Avramis , Sfetsos , Armesto , Edelst ein , Mas , …….
Drag force for heavy quarks in
N
=4 SYM Herzog, Karch, Kovtun, Kozcaz, Yaffe; Gubser, …….
Drag force for a heavy quark moving in the medium: Fluctuation-dissipation theorem Diffusion coefficient: Casalderrey-Solana, Teaney It is possible to analyze the energy flow pattern (indications of conical flow) Note: D can not be used to find
q
ˆ Friess,Gubser Michalogiorgakis, Pufu Fluctuation-dissipation theorem assumes the quark is in equilibrium with the medium: does not apply to high energy jet
Chapter n+1: Quarkonium suppression: predictions for LHC or RHIC II
Quarkonium suppression at high P
T HL,Rajagopal,Wiedemann Techniques discussed above can also be used to calculate screening length between a quark pair. Static quarks : great success from lattice calculation Heavy quarks produced in heavy ion collisions typically move relative to the medium: hard to do using lattice . AdS/CFT: (for conformal theory) See Urs Wiedemann’s talk Heavy quark mesons with larger velocity disassociate at a lower temperature: effect may be significant at RHIC II or LHC
Conclusions: a nice honeymoon
• AdS/CFT provides powerful tools to understand dynamics of strong coupled gauge theories. • Expect
many more
chapters to be written for the marriage between string theory and physics of QCD in extreme conditions.