String theory and heavy ion collisions

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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
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String theory and heavy ion collisions
Son and Kapustas 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
could be explained, and predictions can be made.

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Chapter n AdS/CFT and Jet quenching
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Parton energy loss in QGP
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Wanted a first principle computation of
5-15 GeV2/fm
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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.

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AdS/CFT correspondence
Maldacena (1997), Gubser, Klebanov,Polyakov
Witten (1998)

• N 4 Super-Yang-Mills theory in 4d with SU(NC)

A string theory in 5d AdS
Finite temperature
Black hole in AdS5
Large NC and strong coupling limit

• Classical gravity limit

YM observables at infinite NC and infinite
coupling can be computed using classical gravity
Apply to both dynamical and thermodynamic
observables.
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Strategy

• Need a non-perturbative definition of
• Compute in strongly coupled Super-Yang-Mills
  theory using AdS/CFT

Similar strategy was used to compute the shear
viscosity.
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• Caution
• N 4 Super-Yang-Mills theory is NOT QCD

Later Using sQGP of N 4 SYM to understand
sQGP of RHIC may NOT be far-fetched.
Now Accumulate data points
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a non-perturbative formulation
Hard weakly coupled
Soft likely strongly coupled
multiple rescatterings of hard particles with
the medium
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Soft scatterings
Zakharov (1997) Wiedemann (2000)

• Amplitude for a particle propagating in the
  medium

Soft scatterings are captured by Light like
Wilson lines.
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A non-perturbative definition of
Wiedemann (2000)
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Wilson loop from AdS/CFT
Maldacena (1998) Rey and Yee (1998)
Recipe
area of string worldsheet with boundary C
horizon

• Black hole in AdS spacetime
• radial coordinate r,
• horizon rr0
• constant r surface (31)-dim Minkowski spacetime

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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 !
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Shape of the string
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.
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of N4 SYM theory
BDMPS transport coefficient reads

• It is not proportional to number of scattering
  centers

• Experimental estimates 5-15 GeV2/fm

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Jet quenching in a wind
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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 N4 SYM (not
  necessarily full energy loss of SYM)
• It appears to be close to the experimental value.

Is the agreement meaningful?
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Is agreement meaningful?
N4 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
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Is agreement meaningful? (continued)
N4 SYM at finite T
QCD at T TC -3 TC

• conformal
• no asymptotic freedom,
• no confinement
• supersymmetric (badly broken )
• no chiral condensate
• no dynamical quarks, 6 scalars and 4 fermions in
  the adjoint representation.

• near conformal (lattice)
• not intrinsic properties of sQGP
• not present
• not present
• may be taken care of by proper normalization

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Maybe the agreement is not an accident after
all !
Take
Experimental estimates 5-15 GeV2/fm
Caveat AdS/CFT calculation is in the infinite NC
and infinite coupling limit
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for other theories

• General conformal field theories (CFT) with a
  gravity dual (large N and strong coupling)

aCFT central charge

• Theories near conformal corrections small

Buchel

• Finite coupling and NC corrections hard

Armesto, Edelstein and Mas

• R-charge chemical potentials

Lin, Matsuo, Avramis, Sfetsos, Armesto,Edelstein,
Mas, .
corrections mall when chemical potential is small
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Drag force for heavy quarks in N4 SYM
Herzog, Karch, Kovtun, Kozcaz, Yaffe Gubser, .
Fluctuation-dissipation theorem assumes the
quark is in equilibrium with the medium
does not apply to
high energy jet
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Chapter n1 Quarkonium suppression
predictions for LHC or RHIC II
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Quarkonium suppression at high PT
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.
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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.

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